That's a good approach, and fuzz is an excellent place to start.
Fundamentally fuzz is just overload - clipping the signal. If you put gain in the signal path, sufficient to turn the guitar signal to - say - 10 volts, but then don't let it get that far, but chop it off when it gets to 1 volt, you've turned your guitar signal into a square wave, which is exactly what fuzz is. The normal way to do the chopping is with diodes, which turn on when the signal gets to about 0.6 volts. A pair of those, one facing each way, will result in a signal chopped off at 1.2 volts.
The more gain you put in front, the wilder will be the fuzz. Put almost no gain in front and you have a simple overdrive.