I'm not entirely sure of what you're asking, so I have tried to cover all the angles. I hope this answers your question.
I believe the answer to your question is yes (by either interpretation) and what follows is the rationale for my answer.
Sorry if it's a bit long.
Wizards Receiving wands without the Wand choosing them
It seems to me that it would have to be just the wand choosing the wizard at Ollivander's. If you remember the last book, there was a lot of detail about becoming the master of a wand (so that it would obey you). Based on the fact that one must disarm or kill the wand's previous master to become the wand's new master, we can assume that unless people have disarmed the staff of Ollivander's, that all who have received their wands from the store were, indeed, chosen by a wand.
"The wand chooses the wizard. That much has always been clear to those
of us who have studied wandlore." - Mr. Garrick Ollivander Harry
Potter and the Deathly Hallows
Will There be a Wand for Every Wizard?
From what I understood from the books, it's less of a perfect match and more of a general fit.
"If you are any wizard at all you will be able to channel your magic
through almost any instrument. The best results, however, must always
come where there is the strongest affinity between wizard and wand.
These connections are complex. An initial attraction, and then a
mutual quest for experience, the wand learning from the wizard, the
wizard from the wand."- Mr. Merrick Ollivander Harry Potter and the
So here^ we see how a wizard can use any wand, though the best results come only when "there is the strongest affinity between wizard and wand." Fortunately, J.K. Rowling, not to mention the good people at harrypotter.wikia.com, has written a significant amount on wandlore. Rowling has explained that a wand chooses a wizard depending on how closely the wizard's personality matches the physical characteristics of the wand. I think some information from Pottermore.com may help you with your question.
The following information was obtained from Pottermore.com and was
written by Rowling:
Many wandmakers simply match the wand length to the size of the
witch or wizard who will use it, but this is a crude measure, and
fails to take into account many other, important considerations. In my
experience, longer wands might suit taller wizards, but they tend to
be drawn to bigger personalities, and those of a more spacious and
dramatic style of magic. Neater wands favor more elegant and refined
spell-casting. However, no single aspect of wand composition should be
considered in isolation of all the others, and the type of wood, the
core and the flexibility may either counterbalance or enhance the
attributes of the wand’s length.
Most wands will be in the range of between nine and fourteen
inches. While I have sold extremely short wands (eight inches and
under) and very long wands (over fifteen inches), these are
exceptionally rare. In the latter case, a physical peculiarity
demanded the excessive wand length. However, abnormally short wands
usually select those in whose character something is lacking, rather
than because they are physically undersized (many small witches and
wizards are chosen by longer wands).
Wand flexibility or rigidity denotes the degree of adaptability and
willingness to change possessed by the wand-and-owner pair - although,
again, this factor ought not to be considered separately from the wand
wood, core and length, nor of the owner’s life experience and style of
magic, all of which will combine to make the wand in question unique.
So from this, my personal judgement is that every wand has a general preset and chooses a wizard based on how well the wizard's personality fits the wand's preset such that a wizard could potentially be chosen by a number of wands. Because of how many wands there are in Ollivander's shop, I do think that every wizard is chosen by a wand.
For more information, please click here to visit the Harry Potter Wiki.