Yes they affect the sound overall.
You can get a tube chart from Mesa if it isn't already in your manual (ie. shows you which position V1, V2 etc has an effect on which channel).
V1 is the most important as it is the first preamp tube, the first entry point for your signal. For this position IMHO it is a must to use either a Mesa SP12ax7 ("special") or one from Eurotubes. Not the regular 12AX7.
V2 and V3 are also important. I use a 12AT7 for both of these positions, which is a lower gain tube, about 40% less gain, but very nice and articulate...you may not like the lower gain this produces, but this is a matter of personal taste.
Maybe the best solution for you is to use a SP12AX7 in every preamp location V1 through V5, it will definitely improve your tone.
Also you may try different combinations of power tubes as you can with Road King...try running EL34s along with 6L6s. To me that is a really nice tone, best of both worlds. If you find it muddy you can do what I did with my Roadster: EL34s combined with 6V6s...do NOT attempt this without speaking with Eurotubes first, to determine what to do with yours as it has such a unique power setup - you don't want to burn your amp! They will supply you with tubes that will be safe to use.
Mixing and matching tubes is one of the coolest and fun things to do with a tube amp. I'm sure you'll find your tone.
Also definitely try running your RK through a mesa 4x12 recto standard cab...wooohoooo sweet.