The Twilight Wiki says that female half-vampire hybrids do not produce vampire venom. Males, on the other hand, do and one such male has even turned a human into a full vampire with it.
Unlike vampires, hybrids have a functioning heart with blood flowing through their system.
Having no venom, what would happen to a female hybrid if bitten? Would they turn into a full vampire?
Well, for starters, I don't think the novels ever make it very clear why the male hybrid's saliva contains venom and the females don't; it may be gender linked, it may be random genetics. But that's not terribly relevant, as we can still group the hybrids into two categories: those that don't produce venom, and those that do, and still ask:
If a vampire hybrid that is not venomous is bitten by a vampire, what happens?
The only canonical answer is "no one knows", because it's never happened in the novels, and presumably won't happen on-screen. There is talk of continuing Twilight well past the end of Breaking Dawn - Part Two, possibly as a television series; depending on who they get to write and direct that, we may or may not get some internally-consistent mythology to draw from, and can maybe answer this question.
For now, they best we can do is make an educated guess, based on what we do know about hybrids and vampire venom, and extrapolate that into real-world biological processes.
When injected into a human, the venom attacks their cells and slowly (and painfully) converts them into a vampire. When injected into a vampire, the venom causes some temporary, mild pain. The key questions we need to answer, then, are "What is it about human cells that the vampire venom attacks?", and "Do hybrid vampire's cells have that?"
The action of vampire venom appears similar to snake or insect venom, so lets assume it works the same way as well. Venom attacks the proteins that make up human tissue. Typically, it will attack structures on the cell walls that cause key biological processes to fail, or even the cell walls to rupture. This is very similar to how antibiotics attack bacteria, for example. And just like antibiotics bind better, and thus have more effect against some bacteria than others, vampire venom has more of an effect against human cells than vampire ones. Therefore, it seems logical to assume there is some molecular component expressed on the cell walls of vampire tissue that is distinct from human tissue. (This idea will be reinforced in a bit -- the receptors on the cell wall are a product of the DNA sequence.)
So, the venom most likely attacks something that is found on human cell walls, and not vampire. Would a hybrid have this "venom targeting factor"? Probably not.
(Quick side-note about the genetics. The Twilight wiki claims that hybrids have 24 chromosome pairs; I don't remember that detail but, if true, would almost certainly reflect a genetic defect in the hybrid. There's no way for a hybrid to get an extra pair of chromosomes naturally from a human mother; at worst it would have two extra unpaired chromosomes from the father, and then only if vampires had 25 pairs. If you introduce the idea of genetic defects into the mix, the rest of this hypothesis sort-of goes out the window, so I'm going to ignore it for now.)
A hybrid does not have "human cells" and "vampire cells" -- that's not how genetic hybrids work. The cell has a mixture of genetic material, 50% from each parent, in a combination that just happens to be viable. In order for this to work, the genetics of the two parents must be similar enough that their combined DNA can still code for valid proteins that perform the tasks needed for "life". Presumably, as former humans, vampire DNA is extremely similar to human DNA, so that's good. But hybrids inherit enhanced attributes -- speed, strength, etc. -- that come with being vampires, so those must also be coded within the DNA, meaning vampire DNA must be slightly different from humans. That fits well with the idea that vampire cells are structurally close but not identical to human cells.
Given all of that, I suspect the answer is that lots of pain would happen to a hybrid that got bitten, but probably not anything permanent. Their cell walls would not match exactly what human would be, but would be about halfway (on average) between the vampire and human cells. Thus, the venom would likely find some receptors to bind to and cause cellular disruption, as it does with vampires, only more efficiently. But it likely would not be able to fully bind to the cells and perform whatever transformation process it would against a human cell.
As far as the Twilight series goes, there is no definitive answer because it has not happened. It has, however, happened in other series and would likely similarly in the twilight series. In the Night Huntress series by Jeanine Frost, the main character, Cat, is turned from a dhampir to a full-blooded vampire. In doing so, she gains unique abilities, her diet is not human blood but vampire blood instead and she even has a heartbeat at times. Knowing that a dhampir already has vampire DNA, it makes sense that when turned the dhampir would exhibit unique traits that neither dhampir nor vampire have i.e. greater strength, special abilities, greater speed. This is all speculation as to what will happen to a dhampir who attempts the change. As it stands, I see four distinct possibilities. One, the dhampir's vampire half will always reject the change and subsequently die. Two, the dhampir's vampire half will fight the vampiric infection and be unable to change but will still survive. Three, the dhampir will make the change without any problems or complications and become in all respects a normal vampire. The final possibility is the most interesting and is the one where the change will affect the dhampir in a unique way. Instead of becoming a normal vampire, the dhampir will become an unusual vampire and gain unpredictable traits that may help or hinder the dhampir turned vampire. Again, I'm going to mention that this is all speculation and that this is not a definitive answer to your question.
I don't think the genetics are scientifically based, so discussion is moot. I think it more likely is intended as a possible link in the story of the Twilight books, to continue the saga later. Renesmee has the same number of chromosome pairs as Jacob, making successful reproduction more possible, in terms of thinking about pairings. In Breaking Dawn there was also a brief side plot with Quil (?) babysitting the child he had imprinted on, and having to wait till she grew up, so this is not viewed as an aberration. Also, Leah could possibly imprint on that lone male hybrid from S. America, and this has been somewhat set up by Leah's desire to leave and travel alone. In other words, an entirely new race with two genetic lines to establish that new race, a genetic line that also have includes the ability to mend DNA from the wolves to avoid harmful inbreeding problems, going back go trying to minimally make genetic sense. Personally, I would enjoy more books. I love the character development and concentration on developing gifts and personalities.
