If I feed the subwoofer output signal of my HT receiver(H/K AVR125) to an amplifier(H/K PA2000) which would drive a passive sub, will a crossover be necessary and/or advantageous?
That depends on whether or not your receiver has an adjustable crossover for the subwoofer output. If it does, use the crossover in the receiver to adjust it to smooth out the bass (to prevent humps or dips at the crossover region between the subwoofer and the main speakers).
Alternatively, does anyone see a problem with the following scenario?:
I want to run the sub output(LFE - 100Hz low pass) of my HT receiver to an older stereo receiver(100W x 2), which would become my subwoofer amp. I'd simply split the LFE output signal into the R/L CD input (for example) of the stereo receiver, then connect each output channel to a coil on a 12" DVC subwoofer. I am assuming there would be no phase issues with the signal from the stereo receiver, since the LFE input signal would not be stereo.