Yes, everything I've flown you can simply put the engine fire switch or handle back to it's normal position and restore all fuel, hyd, bleed, etc to the engine, thus allowing a restart. Obviously only going to work if the engine isn't damaged or just plain broke.
If you shut a motor down for things like excessive (but not ridiculous) vibes, or hot/low oil good chance you could restart it.
Having blown the bottle shouldn't affect a restart. I don't think bottles blow into the core flow path anyway and if it did it would be flushed out in a split second during flight.