I do it regularly. The only problem I have ever had with using undersized tubes is if trying to run supper low pressures they don’t put as much pressure on the bead allowing the tire to turn on the rim resulting in a sheared off stem. You could glue one bead on if you have that problem though.
You also get a different feel with a different tube in your tire, some like the feel of the smaller tube, some don’t. It is a pretty cheep experiment to try.
I personally dislike a smaller tube. it requires a higher pressure to establish the correct tube size to fill the tire… and makes the uni feel totally different and much less responsive in my opinion. to your account, if the tube is sized exactly 2.5", it will probably work fine, but if that is the max size I would try something different. if you cannot find the proper size, check out a motorcycle shop, but there you will need a 22" x 2.5(or 2.75, 3.0 is probably too large)" tube (they measure outer rim diameter, we measure outer tire diameter)