Do it. I used to have a hybrid (
a trace elliot supertramp) which really reacted to different BRANDs of tubes, not just types. Assuming you are talking about a hybrid amp?
I tried heaps of different 12ax7s in there and it really did change the character. Ruby Tubes, Groove tubes, Sovteks, JJs, mesas (and some other rebrands)... I think I liked the JJs the best as usual. At the end of the day it wasn't enough and went all tube. Each manufacturer makes them slightly different so you get different flavours... but remember lots of tubes are simply rebranded (like the aforementioned mesas which are just chinese tubes graded for their amps), so swapping an EH for a sovtek won't make a real difference (or much of a difference).
I guess it's down to what style or sound you're after, but cleaner types (like the 12at7 or 12au7) might not suit if he's after more crunch; but yeah as above it depends on the amp design as to how it will affect the entire sound.
If you're talking about an all tube amp; changing the FIRST preamp tube often makes the largest difference in my experience. Leave the phase split tube as a 12au7 or 12at7, you don't want to hot that up. Otherwise honestly a fresh set of power tubes and a bias helps far more than changing your preamp tubes, but again that's only for all tube amps.
Check out eurotubes.com for great tubes and a lot of good info and service. Bob grades the tubes according to your taste; so if you want it a bit hotter he can do it; I've bought lots of tubes from him and he's always great.