Sure its possible to add fuzz. Its basically the same thing as sticking a fuzz face or similar unit in front of your amp. So build a fuzz face circuit on the input inside your amp, make it switchable so you can turn the effect on or off, and you're good to go. of course you could just use a fuzz pedal and build a good sounding amp too. BTW, overdrive is something that happens naturally in tube circuits when the gain coming in is more than the tube can amplify cleanly. Tubes can't keep up with the demands placed on them by such a large input signal, so they do what they can, and then they start to distort and compress, which generates lots of 2nd harmonic and to a lesser extent, 3rd harmonic, and all of that serves to fatten up the sound and makes it much nicer to play than a cleanish solid state amp. One last thing, if you've nver built an amp before, starting with a simpler circuit such as a champ or similar build is a much wiser course of action than jumping right in and building such a complicated amp.
Greg