I think you can divide the effect of tubes up into a couple of areas:
1. Cosmetic: lots of low end gear throws in a tube, it's operating at low voltages and sounds nasty if pushed, so it's there basically to glow (some signal is sent thru it and it might amplify a little but it's not adding harmonics).
2. Drive: some gear uses a tube to introduce harmonics by pushing it. This can be a good or bad thing I guess, depending on how well it's implemented. Something like a Millenia hybrid or the UA stuff does it really well, I'm sure.
3. Compression: tubes naturally do a nice job of compressing as you push them harder, although the THD levels go up as you do this, some pres and even mics rely on this.
Bottom line is that you're going to have to try out gear to see if it does something you like to the sound. Either test it out at the store, rent the gear or buy used and sell if it isn't helping...