I don't think they'd be allowed round for a "visit" to see if they get on with your two as that's not the way introductions in a multi-cat household should be made. If all the cats are suddenly confronted with each other it probably won't go well and could be traumatic for them all.
IME (many years of multi-cat owning) you proceed very very slowly by confining new cats to one room for at least 7-10 days. After a couple of days swap bedding about so all the cats get a whiff of each other's scents IYWIM. Then, what I do is bring new cats down to another part of the house, e.g. lounge, but have them shut in there for a few hours, with me, so again, they get to explore a bit more and also leave their scent .... before returning them to "main" room. Then next day, introduce them somewhere else and so on and so on, obviously making sure they can't get out at this point. Personally, I've had "new" cats in the house for 10 to 14 days before letting new and "old" meet and so far, it's always seemed to have done the trick. I introduce one existing cat at a time - starting with most laid back/placid - and for short periods, always with me there too .... and again, gradually increase periods of time they spend together before separating them. When doing these introductions I also remove "new" cats (back to their main room) first because I believe psychologically this helps existing cats feel more secure, as well as new cats being reassured the place they know best is still there IYWIM. And it goes without saying that at the very first sign of anyone being stressed you separate them - there's no point in forcing the issue - you can always try again the next day.
Anyway - I've either been incredibly lucky and/or must be doing something right as all the cats I've introduced have got on well together. I currently have 4 boys for example (+ 1 girl) and was worried before about territory marking, aggression etc but honestly there's no issues at all and they often all sleep together!
Having said all that I've always been guided by what the shelter advises - there's absolutely no point trying to merge animals who've already showed signs of disliking other cats. Indeed, some cats won't even tolerate a single other animal. And of course, however careful you are, there are no guarantees ...
... but having said all that, there'd be absolutely no reason why you can't talk to the shelter about this (providing your DP is also on board of course). They'd almost certainly be delighted at your interest given how older cats are so often overlooked. Hope it all works out for you.