they would ruin your homer's homing abilities. well, not the adults but the offspring will not have great homing abilities. They will pretty much be called barn-pigeons (scrubs) an lose their value.
Please don't mix them!
I think they all have it,its just more pronounced in homers. I raise rollers and have had them come long distances when they were sold or given away. Doesn't always happen. Have had others get lost a half a mile from home and take up with wild flocks! Like the other guy said ,I would not mix as it will ruin the valvue of your purebred birds. If you still want them,pen them separate and use them as feeders for your homers. Wild pigeons are just as enjoyable as the fancy breeds. Thats what I started out with some 45 years ago!
I wouldn't do it for all the reasons above... However if you decide to go ahead and do it anyway, just think about all the fun and exciting diseases you'll get to learn about, it will be an opportunity to learn about sorts of interesting avian diseases that captive pigeons can catch from wild flocks... Yes i'm sarcastic, but please don't take offense. What you are thinking of doing is kind of like adopting a wild raccoon as a friend for your dog.
Those pigeons are used to being free. Taking away their freedom would be cruel. Lots of people look to give away free Homers. Because you can only fly the babies, many will give away their breeding stock when they have enough birds.
Who says you can only fly young birds? There are both young bird and old bird races. Wild pigeons (in addition to many other diseases) frequently carry a virulent form of canker that is almost 100% fatal to captive raised birds. There would be no common sense reason to combine wild birds with an established flock. Unless of course you wanted to infect and lose all of your birds.
I was told that all the wild pigeons were once domestic homers. That excaped and went feral.
To prove the point to a friend once. I caught some wild ones. And entered them in the fair with my bought ones. Some of the wild ones won better ribbons than the ones I had owned for years..