I advise against it. What I suggest is, you partition your boot drive into one partition, containing FCP7/ FCS3 apps and the OS you're on NOW... and make a second partition on the boot drive, the home for for Mavericks OS and any modern apps that need it. Heck, put FCPX and Compressor and Motion on there, and start learning them.
Some daredevils have run FCP7 in the Apple MavericksOS and even in the beta version of the upcoming Yosemite OS, and reported it still works, but the other scuttlebutt I read is that little things around the edges of FCP7 have issues or failures in those environments, for which it was never designed. but if you want 7 to work fully as it was intended, I believe you need to box it up in it's own drive partition and leave the OS at around 10.6.8