No, not a second logged-in player profile, I'm talking about peripheral profiles.
One logged in player profile toggling, using the Xbox quick menu, between multiple peripherals, each set to its own saved peripheral profile.
It's a system level xbox feature, been there ages.
You can save multiple peripheral mapping profiles. so say you want to toggle your pad between having the triggers and face buttons swapped, or invert the y axis on one stick or the other, etc. You save a profile with all the control settings remapped how you want. It's super handy for, for example, games which don't let you remap the control scheme AT ALL. I used it to create a profile which I load up any time I play Rebel Galaxy Outlaw where all the controls are mapped identically to ED's inputs.
So theoretically using that system you could potentially make sure that however the HOTAS is laid out, its profile's inputs map to the same ones as the pad's default profile. I can't say for sure as I haven't seen an XBox HOTAS I'd feel comfortable with the build quality of yet, but in theory it should work?