it will only sound as bad as you want it to sound. A guitar amplifier should be fine for most things, you can even growl up the lead sounds with judicious use of gain and a little reverb never hurt a lot of synth sounds.
Just go easy with the gain stage - don't introduce distortion on sounds that don't cope well with that kind of effect (strings, pads etc) by all means go mental on leads and basses however, they can sound really good.
Also careful use of distortion on electric piano and organ sounds always adds some welcome colour.
I used to use a wah-wah pedal, a phaser or a roto-vibe on a fender rhodes sound all of which was then put through a screamingly overdriven Vox AC30 and it sounded coooooool.
If you're recording try taking a dry signal to one channel and them a miked signal from the overdriven amp to a second channel and the blend the two until you get something really sweet.
Enjoy.