So the answer does depend on the amplifier you are using. Yes the whole impedance thing is very important first and foremost. Yes, you will get a bass sound out of the amp without doing any damage. The extent of how useful the sound is does depend on the amplifer though. As noted above, some guitar amps DO have a big roll off in the lows so when they distort, they don't sound mushy. That's not always good news for the bass player though. Our power is in the lows. Sure, you'll be loud enough but you *might not* get trousers flapping.
It is true that quite a few bass amps share the same circuit topology that guitar amps do with *but* minor tweaks. I have a '68 Marshall Super Bass, which as I understand it has probably £1 worth of component changes (if that) to make the Marshall Super Lead model suitable for bass, hence the name change. Oh and how does it sound?
Luscious! I had a recent service where some components were further uprated and I am very surprised at how much low end can come from such a simple amp design.
In response to the comment about StickelBack - The bass player uses guitar amps in parallel with bass amps to get an aggressive bass sound. So the guitar amps aren't deploying the earthquake part of Mike's signal. I only know this as it was asked reacently on the forum.