Yes and no.
The 500 Caddy is a BOP (Buick/Oldsmobile/Pontiac) bell housing is it not? If so no adaptor is required. As I stated before, these transmissions were used in full sized cars in the late seventies when GM downsized all their big cars. My co-worker had a Caprice wagon with an Olds engine in it from the factory, so BOP 700R4 transmissions are out there.
4L65E mechanical upgrades are commonly installed in 4L60E transmissions which is an electronic valve body version of a 700R4. 700R4 is not electronically shifted and works with carbed engines with only the addition of the TV cable and a lock up torque converter switch. No stand alone computer is required for the 700R4 transmission.
700R4 transmissions are used behind big blocks in aftermarket applications, so I am sure you can make one live behind the Caddy. Check out Bow Tie Overdrives and some other internet vendors of these transmissions.
I looked online yesterday and a Gear Vendors is 3500 dollars new, so a transmission is still cheaper than a new Gear Vendors Overdrive.