This is exactly how mine is set up. My lift pump pulls thru my facet pump (mounted on frame) just fine. I rarely use my auxillary electric pump but it has come in handy multiple times. I have a switch near my HHO gauge and flip it on when I need to prime system when I change fuel filters and injectors. When I did injector job (twice), I flipped on my aux. pump for about 2 minutes and it started like I never even touched anything. My setup doesn't seem to interfere with the lift pump at all and am pleased with the setup.
Good to hear. Do you have a thread with your setup? What pump are you running?