I've done it several times in multiple generations. However, in the Advance Generations there's a major problem with it.
Double Battles.
You can skip most of them, but what about Liza and Tate? You'll need to have at least one HMer who can put up a decent attempt at battling when needed, or else every double battle you fight will involve the foes picking off your HMers and then ganging up on your battler if it hasn't finished them off by that point.
For Advance Gens, I have to suggest a two-fighter challenge instead of a single-fighter challenge. I'm thinking about restarting Pearl Version and going through with just a Pachirisu (for high-level Pickup), a Shellos/Gastrodon (to balance out types somewhat) and some HMers.