No, that's not how it works. The guitars in game are as far as I know only for aesthetics. Each song is still tabbed properly, despite how many frets your guitar has. You can try bending the 20th fret to play the same sound as the 21st fret. However if the 21st requires a bend, that's tough to make the game register.
But in reality, get a guitar with more frets. 24 frets is the minimum I'd have on any main guitar.