You can have the passive immobiliser setting turned off in the BECM, then you should be fine to have the RF receiver completely disconnected. I would just make sure you have a good drivers door latch - as you will be relying on the microswitches in that, and if one of the CDL or Key switches starts having issues, then you can still end up with a pile of headaches.
Luckily on the later P38's (BECM Software V36 onwards) you can enter the EKA via diagnostics on the OBD port, so a bad door latch isn't as bad as the earlier P38's.
On the key fobs - they are programmed/hard coded from the factory with their ID - this is stored in non-erasable memory. If you take the batteries out it will lose sync to the vehicle, and this will need to be re-done via the key in the door method, or if passive immobilisation is turned on (and the coil around the ignition works!) then it should do it automatically. One important note on key battery replacing... I advise all owners to replace the batteries in the fob with the vehicle UNLOCKED... mostly because it then avoids potential headaches of the vehicle needing the EKA before it will then resync the key (which numerous owners have then found they don't have the EKA, and what should be a simple job turns into a total headache)
But that aside - and back to the OP's problem...
Disconnect the RF receiver and see if that makes a difference in your battery drain.
Have you tried sitting in the vehicle in the evening with the RF receiver still connected (doesn't need to be locked) and see if the BECM actually goes to sleep, and if it does, then if it is woken up again by itself. This only works if you have an auto, but looking closely at the gearshift, you'll see the selector LED faintly lit (next to the 'P' if in park!) when the BECM is awake. This will extinguish if the BECM is asleep.
Sit and wait a couple of minutes and see if the light goes out. If it doesn't, then try disconnecting the RF receiver completely and repeat the test. If it then goes out, RF is your issues and causing the BECM to stay awake. If you disconnect the RF receiver and the BECM STILL doesn't go to sleep, then you have something else causing your battery drain.
Likewise - if the RF receiver is plugged in and the BECM DOES go to sleep, and it ISN'T woken up again (red light comes back on) then RF ISN'T your issue, the BECM is sleeping, and there must be a battery drain somewhere else (whether BECM related or not).
try this out and report back, as it will help narrow down/prove/eliminate area as to where the issue actually lies.
Marty