A rehab center will KILL the Pigeon. We already know th bone is badly broken....I guaramtee you a rehab center will NOT go to the touble of attempting to mend the bone and then care for him/her and try a release.
So, basically....your choices:
1) if you bring to a rehab center they will say he is unreleasable and put hime/her down. Period.
2) So the next question is now: can you convince the vet you went to to try surgery ? If they balk, as them for another Avian vet recommendation.
You know, it is surgery yes, but quite honestly...pinning a broken wing bone ? It isn't crazy complicated, usually.
Then there is what you asked:
3) Do not proceed with surgical possible cure and just have the vet properly wing wrap the wing (this will require them to be sure that everything is aligned as best as possible, it may well require an x-ray from 2 angles, post-wrap; I say this because once a vet - well-meaning - wanted to save me some $ and did a wrap witha single x-ray view; only we discovered 4 days later that the bones were only aligned in that view, a rotated view showed she had missed alignment completely....eesh; but the story ended well, ultimately).
The wrap would need to stay on for quite a while...around 6 weeks I think, if memory serves.
Wound/scar tissue will begin to generate and it will...to a certain degree...bind things together a bit and stabilize the area some.
Supplemental meds will need to be given. An antibiotic to prevent infection, and they should also provide a calcium supplement..and perhaps a painkiller (metacam) would be nice for the first week, too.
However, although the joint will mend some and stabilize...flight returning ? Not likely; certainly not to the degree of releasing back into the feral world. Best case scenario there is a condition which a number of my rescue loft birds have : partial fight ability, able to jump-fly short distances of maybe 5-10 feet and the capability to get from the ground to a nest or perch or shelf maybe 5 or 6 feet off the ground. Not bad, but certainly not anywhere near the ability necessary to live a Feral existence.
So, THIS option comes with the expectation that from hereon in, the Pidge is now yours (or You are His/Hers). So you can keep as a pet (he/she will acclimate to the indoor life, certainly and they ARE great companions), OR you can build an aviary for her/him and maybe do some indoor-outdoor sorta arrangement.
My bet is...in a short time, you will actually come upon another feral in need, some way or the other...so perhaps this can be the beginning of something for you. So I say that because the first notion which often comes up at the suggestion is: "oh, that's so sad, because he/she will now be alone and with no other Pidge friends, forever...it's not fair to the Pidge".
To which I say 2 things:
~ You and he/she crossed paths, Pidge would be dead now if not for you
~ Given that has happened, who are we to decide it is 'wrong' for the bird to live ? To make the determination that it IS fair to put him down ? Seems quite specious....
So, again, you keep him/her, and I would say there is a likelihood that down the road some....you may encounter another which turns out to be unreleasable as well. It's quite possible.
But those are your only real choices.
If you are open to the expenditure....I say find out more about possible surgery. I have spent upwards of $500/ea on several injured ferals over the years...most were actually ultimately successfully healed and re-released. But if that isn't possible, then either you now have a companion, or the choice of putting him/her to death is now yours (because at a rehab center, the result is foregone - they will not bother with mulling over such a choice, am afraid to say).
Thanks for caring and helping the Pidge.
(BTW not sure what happened with representing him/her as a pet...but in any future talks with any other vets, represent the Pidge as your pet. Even if they push you to say he/she is a Feral, stick with your story. I know, it shouldn't MATTER to them, as long as you are paying - and I have been fortunate to have avian vets over the years who took this exact position - but to some, they will try to get an admission that it is Feral and therefore they will deny treatment...I know, nonsensical)