Since the .38 won't be recessed, it should work just fine. If the reamer has a recess cutter, you'll be stopping before you get to it. Like you said, be careful not to go too far and keep all chambers as close as possible to each other as far as depth goes.
Lots of cutting oil, clean the chips out often, go slow, and remember, you can't put any metal back once you remove it.
I've successfully rechambered .22 chambers to .22 Mag by hand and it worked great.