Actually if you want to find out for sure if your iMac has the ability to run in 64bit then please open a Terminal session and copy and paste:
ioreg -l -p IODeviceTree | grep firmware-abi
paste it. If it returns EFI64 then it will run in 64bit just fine. However if it returns with EFI32 then the previous poster was correct.
Thanks for all the replies, folks!!
The terminal commands returned EFI64, so I'll make a Lion installer drive and give that a try on a backup and report back.
I found a post about Mountain Lion compatibility on another forum that said that the 7,1 model was
64-bit capable but disabled in firmware when released until more developers had a chance to update
their apps for 64-bit compatibility.