Any modern CPU can still support a 32bit OS. So no matter what i7 you have you will be fine. Also note that Araas is correct you will be limited to a 3GB usage of ram so if you wish to have more you may want to move up to 64bit.
On a side note if you are afraid of compatibility issues with a 64bit OS then why not consider going with a dual boot system? Windows 7 can be 64bit while XP of course at 32bit. Simply use XP for the programs you find to be incapable of running otherwise.