Depends on the dimmer. Older ones would be rheostats or variacs (which were bulky).
Modern ones are FET (Transistor) based and need the AC signal to regulate I believe. Not that familiar with the internals myself on that one. Plenty of schematics, and a few different ways to do it, but most I see use a DIAC and TRIAC.
TRIAC dimmers have been around for quite a while, my mother has a 30+ years old one for her dining room. You wouldn't have a 500+W rheostat or variac in a standard electrical switch/outlet box.
Using a dimmer with a switching AC-DC power adapter isn't going to work particularly well, the harsh current spikes may cause the input capacitors to fail prematurely. The dimmer itself may also take offense to switching into a capacitive load.
Using a dimmer with a traditional iron core transformer could also be a little problematic due to the inductance possibly not allowing current through the TRIAC to rise fast enough to keep it on after the initial turn-on pulse fades out, an RC circuit in parallel with the inductor may be needed to smooth that over.