It'll work just fine. Mountain Lion is probably the most trouble-free OS upgrade I've ever seen them come out with. You should notice a slight speed increase in day to day stuff too. Make sure you upgrade to the latest parallels though. BTW If all you're using Parallels for is one app, make sure you don't set the RAM too high and take away from the OS. Two gigs of RAM for Parallels should be more than enough. You can probably even get away with a one gig setting.
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