By default the sub always gets the LFE channel on most setups - if you have a crossover set (ie: mains are not full range) - then the sub "should" also get the part of the frequency range from the Mains which is below the XO point.
But when the AVR is set to "stereo" - then bass management may or may not be involved, depending on the AVR setup.brand etc...
Most AVR's also have a Direct or Pure-Direct mode - where the channels are passed through untouched to their respective speakers - typically that should disable XO's and if fed a simple stereo signal should output only to L&R.
The other thing to watch for, is how the sub is hooked into the system - so far I have assumed the sub was connected to the Sub output of an AVR, but lots of subs have alternative options - my Gallo sub has an input and an output for the L/R mains at speaker level, and then it acts as the crossover (adjustable for frequency, level and phase)...
If your sub is set up this way - with the XO being in the sub, then all signals fed out, will result in sound from the sub (depending on LF content obviously).
