Varying MCU supply voltage

My question is whether it's reasonable to expect reliable MCU operation with the supply voltage going from a minimum of say 2.7V to 5V, and then back, or is this just a Very Bad Idea?

I would think it should work ok. The only caveat I can think of is that the brown out voltage detector reset might have to be disabled or set to a value lower then 2.7?

Lefty