Unclear, but there's no evidence they would survive.
As an initial point, none of the games ever mention anyone having survived a mating with an Ardat-Yakshi, and it is repeatedly stated that mating with them is invariably fatal. The games also do not discuss any matings between two Ardat-Yakshi. So my baseline assumption is that both would die.
In Mass Effect 3, we visit an Ardat-Yakshi monastery. It is not entirely clear what life in the monastery was like, as it has been largely dilapidated by the time Shepard and company arrive. However, several of the audio and text logs that the player can find indicate that:
- The Ardat-Yakshi were not allowed to see the vid Vaenia, which is mentioned in Mass Effect 2 to involve "glamorous asari" (and is insinuated to contain adult or at least romantic content).
- They were forbidden from visiting each others' quarters or meeting with one another anywhere without supervision.
- They were denied access to the extranet, but only after "Reaper rumors" began to circulate.
- Their schedule was quite full, having only two hours of free time per day (plus meals, sleeping, etc.). The rest of the time is occupied by a mixture of classes, "study periods," chores, and meditation.
- One of the Ardat-Yakshi was denied a supervised visit to Thessia on the basis of being "a romantic."
- All of these rules were very strictly enforced. Repeat offenses were to be "met with confinement."
- At least one Ardat-Yakshi actually was confined, but only after attacking her guards, possibly as a result of trauma inflicted by Justicar Phora during capture.
Based on this evidence, it appears that the staff did not want the Ardat-Yakshi to mate, and also wanted them to focus on their studies and meditation rather than sexual or romantic ideas. There are several possible reasons for this:
- Sex might prove fatal for one or both of the participants.
- Samara says the Ardat-Yakshi become addicted to mating. Any mating, even a successful one, might interfere with voluntary abstinence.
- The Ardat-Yakshi shown in Mass Effect 3 may have been too young by asari standards for mating (or viewing adult content) to be morally or legally acceptable.
Although this is inconclusive, it is striking that Ardat-Yakshi are not simply paired off into monogamous couples and quietly disappeared to some backwater asari colony to live out their lives in peace. If they could mate without consequence, this would be a far more straightforward course of action than the monasteries (although it would require a certain amount of clandestine supervision, the asari are very accomplished at intel and reconnaissance).
Out of universe, the Ardat-Yakshi very loosely fit into the vampire genre. The genre conventions for vampires feeding on each other are unclear to me, but in general:
- Vampires usually derive their immortality from the blood or life force of mortals (i.e. the regular people, or in some works, livestock, that they feed on). As an example, consider the "side effects" of repeated feeding which Stoker described in Dracula.
- Logically, then, they should have no life force of their own, save for that which they have stolen from mortals.
- Depending on the work, it may or may not be possible for a vampire to reappropriate this stolen life force (e.g. Dungeons & Dragons 3.5e says vampires can "suck blood from a living victim", but Pathfinder has no such restriction, which I found rather surprising given how close the source materials are).
- However, I'm not aware of any works which allow the vampires to feed on one another indefinitely without feeding on mortals at all. That would make little logical sense to me because the life force has to come from somewhere. (Yes, the Pathfinder rules do allow this, but those are gameplay, designed for short combat encounters. It seems unlikely that the mythology of Forgotten Realms or the Pathfinder setting actually permit this over extended periods of time.)
- Some works (e.g. Stargate Atlantis) also allow the vampire to return the life force, voluntarily or otherwise.
(All of the above points are generalizations, and of course there exist counterexamples to each of them within and throughout the vampire canon.)
Much of the above discussion is inapplicable to the Ardat-Yakshi. In particular, their long lives have nothing to do with the number of people they murder; they are long-lived because all asari are long-lived. However, genre conventions do suggest that the Ardat-Yakshi ought to be unable to mate with one another in the first place, or at least that they should derive no benefit from it.
Meanwhile, there are writing problems to consider. If the Ardat-Yakshi may mate without consequences, then most of their moral complexity goes up in smoke. So on the whole, out-of-universe considerations strongly counsel against the Ardat-Yakshi being able to mate with each other safely.