There are always dangers when dealing with "questionable" power.
It is always a good idea to have conditioning between you and the source. The best you can afford is a good answer to the next obvious question. Furman products are industry standard.
That being said, the vast majority of audio gear used on stages is usually not connected through power conditioning. From stage gear, right up to PA power. You can get away with that if someone checks the power source to verify it's integrity.
The biggest thing that will affect "performance" of an amp will be starving it of power. Running too much gear from too small of a source. I just experienced a little bit of that at "Salty Jam", with the old... task lights dimming when the kick drum hits...
That's a case of the rig not being connected to a large enough service to feed what was being used. Still not near being dangerous to the equipment.
Saint John typically has good power. It's the temporary hookups for shows that are the biggest x-factor. I was just talking to Blake from the Playhouse in Fredericton, and he was telling stories about how bad the power is in that part of town... doh!
I'm sure oddioguy will have some to add to this.