In the late 80's, I had an instructor in BMQ (aka boot camp) who told us that 7.62 NATO picked up off dead NATO soldiers could be used in Russian AK's. Even then, I knew that AK's used either 7.62x39 or 5.45x39. I had a hard time keeping my mouth shut on that one (laughing at an officer is usually NOT a good idea

).
He was a 2nd Leftenant, if anyone's interested.
That said, 7.62 NATO would probably feed into a Mosin-Nagant, but I shudder to think how inaccurate a .308 bullet going down a .311-.312 barrel would be. Might be kind of hard to extract, since the 7.62x54r is a RIMMED cartridge and 7.62 NATO isn't (meaning the extractor probably won't grab the rim).