I'm no expert but I'm willing to bet there's a unique Serial key or something for each disc, that ties your disc to the install on your Hard drive, so you can't do what your suggesting. I'm pretty sure the game disc still needs to be in the PS3, in order for it to do the verification to allow you to load off the hard drive, or at least what ever frequently accessed data it installed to the drive.
basically same thing many PC games have been doing for years and years now.
ever notice how you can install a CD or DVD based PC game to your system, takes up more drive space than what the disc can hold, and still requires you to have the disc in drive? its because it does a verification that you own or have the disc for the game, then allows you to run the game after its verified you have a "legit" copy.
there's a reason a lot of those No CD files or tools for certain games are Called Cracks or hacks, because they do just that, a hack to skip the disc verification process and load the game with no disc in drive.
I'm pretty sure the Sony PS3 uses some similar process for this.
when it comes to Copy Protection and the sort, Sony's not known for being lax in not supporting Copy Protection on their Media...
some may remember something called SecuROM, thats still out there and used today. MiniDisc ATRAC3 Audio Format anyone? the list goes on and on.