Since LED's bulbs are, by definition rectifiers ( I believe they are
full wave) would it be possible to use them as such by putting a
standard light bulb socket in a circuit?
No, they are not full wave rectifiers....
They are rectifiers but, the purpose of a diode rectifier is twofold; one to conduct current in the forward direction (LEDs do that) AND block voltages in the reverse direction (ordinary diodes do that easily but most LEDs breakdown after a few volts). This almost certainly means that LEDs will destruct on anything other than a low voltage AC circuit - maybe 3VAC maximum and, this is no good in the application the OP considers.
The 2nd question I cannot answer BUT, it ought to be asked seperately because I don't see a connection in anything other than the use of the term LED. The connection with LEDs is as tenuous as it comes I believe.