If I had to take a guess...I'd say that you're going to have a 99% chance that it's going to work.
Since the e46/e39/e38/e53 were all built during the same production range and have basically the same options & features built upon the same BMW electronic communication bus...again, a successful outcome is eminent.
I installed an e38 EC rear view mirror in my old e34 525iT and all of the mirror stuff worked without incident. That scenario was similar to yours in that the e34 had a plan non electrical rear view mirror. But when I pulled the sunroof access panel...there was an electrical harness tied off in a bundle of wires above the headliner which mated up with the electrical plug in the e38's EC rear view mirror.
The only thing I had to work around was finding the wiring pins that controlled the central locking (FZV) because the e38 & e34 had different central locking set-ups. The e34 had older generation locking system used in the e32/e34/e28/e23/e30 era. More than likely this won't be an issue for you due to the same communication bus set-up between the e46 & e53.
If you were trying to use a mirror from the e38...you may have to switch/pull the wiring from the electrical connector for the DWA (anti-theft alarm) red LED since the e38's LED is located on top of the dash instead of being incorporated into the "clown nose" on the bottom of the mirror.
Please do keep us updated to your outcome.
TIP: dont' forget to cover the sensor (like with your finger) that faces the windshield when testing the sensor on the front of the mirror with light. The sensor on the rear of the mirror (the ambient light sensor) is used to darken the mirror as well as the one on the front. The ambient sensor tells the mirror that it is dark enough to dim if bright light is shined on the front sensor.
(the pic below is from my old DIY upgrading my e34 with an EC mirror from an e38...the EC mirror wasn't even an option for the E34 Touring...but the wiring was there and plugged right in to the EC mirror...the only wiring pulled from the harness was for the central locking system which was different between those 2 model's generations)
