Hi, just a few comments. If one of the diodes in the alternator (the diodes convert multi-phase AC that the Alternator makes, into pulsating DC) shorts or goes to a low resistance both ways (still bad!), the alternator could still develop some power. Those diodes are always connected. When the engine is OFF, they can drain the battery down via the alternator output lead, through the bad diode, to ground through the guts of the alternator. I had this happen to me almost 20 years ago. Had to disconnect the battery Positive lead each time I parked until I could replace the alternator. Took the old one apart, and found one of the diodes shorted and overheated, un-welded itself, and tacked itself back on next to where it usually sat on the heatsink.
Back to that part above about "pulsating DC". Don't disconnect the battery while the engine is running. Without the battery there acting like a big capacitor to smooth those pulses out into nice DC, your electronics everywhere on the vehicle are getting slammed hard by high voltage pulses. Not good - can lead to real problems, expensive ones!
With the engine OFF, disconnecting one side of the battery, and putting an ammeter in series, can tell you about drain while OFF. For many vehicles now, they draw some, till the electronics goes to sleep after a while, then the drain really drops, but there always is SOME.
Without looking at a wiring diagram, I can't say for sure about a sticking relay, but you're probably right, in that is another drain that can happen.
If you suspect the Alternator, disconnecting the fat lead from the alternator to the battery, putting Ammeter in there in series (all with engine OFF), will tell whether the alternator output diodes are draining the battery. Should be zero drain there, if all is OK.
That's my 2 Lincoln's worth