Everytime I park my car at my house I take the faceplate in the house with me. If someone were to break in my car and take the head unit (no face plate) would they be able to buy a new face plate and use the head unit? Is there some kind of unique "ID number" or "connection" between a head unit and its faceplate?
Not really, you can buy a new faceplate for the unit model, Ordering a faceplate from the deal cost about 150, but on ebay it only cost about 60 buck, now day people still any kind of head unit, face/ or no face, they can get the part easy
That's why the blinking red LED is somewhat useful in those headunits with removable faceplates. Additionally, the detached faceplate can still deter wannabe thieves from stealing your head unit.
It's better that you take it off anyway. There are few people I know who have had their head unit stolen without the faceplate, but many who have had it stolen with the faceplate on (even a mid-nineties model of a Sony cassette head unit).