We disproved that on the Atmega328P.
The discussion here is about the ATtiny85, and the ATtiny85 data sheet claims that edge detection on INT0 is not active during sleep. I'm sure the OP would be happy if this were proved to be incorrect!
However, I'm not clear on how one would actually test this. A high-to-low transition would end up low, so "falling edge" and "low level" interrupt would appear to be extremely similar if not identical. The same consideration would hold for the attempt to distinguish "rising edge" and "high level" interrupts.
Maybe some clever tricks with a logic analyzer could distinguish the cases.