I do this too, even for medium CAD applications (electronic schematic and pcb work).

That notice was for the physical card itself, not the number: http://www.straightdope.com/columns/read/141/why-does-my-old-social-security-card-say-it-cant-be-used-as-id

Although they would be tested as a system, the rules for each piece would still be different. For example, in my Wayne-Dalton system, the remote transmitter has its own FCC ID: KJ8HHT-3720. You can see from the block diagram on the FCC site that it only includes the transmitter, not the receiver. It would be difficult to argue that the receiver isn't a digital device - anything with pulses over 9000 per second, and "using digital techniques" qualifies - how do you think it decodes the transmitter key codes? Just because it has a motor drive doesn't mean it's not a digital system.