Any watch out for's
Probably not, I've put a 622 x 23 trainer tire on my son's 29'er that we use on the trainer while indoors. It has a 622 x 20 mm rim on the rear. Normally for outdoors that would be a 622 x 54 mm tire which is advertised as 29" x 2.20" as part of it's name in the big white letters on the sidewall.
For real cycling not on a trainer I might be a little leery of running tire that is close to the same width or less than the internal width of the rim. So I'd either tone down how aggressive my riding is till I figured out how well it handled, or I just get a wider tire.
Also, running those narrower tires on too wide a rim might expose you to more rim damage if you should ever flat.
Learn how to find the ISO sizes of tire and rim and you won't have to wonder what will and what won't so often.
As to your original OP, tubes should not exceed the inside diameter of the space created by the rim and tire. If they wrinkle and you ride them then that will be a point for wear on the tube and you'll probably flat sometime in the future. Tubes usually come in a size range of widths they'll work in and sticking to that ensures the tube will not be over size for the tire. But for times I don't have the proper tube, I'll put anything I can stuff in there so I can get to where I have to get.