Seriously doubt this would work without AirParrot or the like. AirPlay Mirroring on Mountain Lion needs Intel Quick Sync Video supported in hardware (note the "Calm down" is part of the article title, not a comment directed at you):
Calm down, 10.8's AirPlay restrictions are technical - not planned obsolescence
In order for AirPlay Mirroring to work VMware Fusion would need hardware support for IQSV for OS X guests. Given I don't believe there's hardware accelerated video for OS X guests, IQSV (which probably is above and beyond hardware acceleration) likely won't work either.