First a little background. I'm finishing a bathroom in my basement that was roughed in while the house was being built. I have a sump-pit that needs to be vented. Due to hvac and plumbing obstructions, I will need to extend the plumber provided vent pipe from the floor above a few inches below the floor joist and elbow to the next joist over so that I can connect the sump pit vent pipe. This will produce a situation where the vent from the sump will make a drop down into the existing vent and back up again. Sort of an oversized p-trap.

Will this work? I have included a rudimentary diagram for a little more clarity.

I've looked at your diagram. You just can't trap a vent and especially a holding tank vent. This vent has to vent both in and out so a AAV,(air admittance valve) is out of the question. Reconfigure the vent and eliminate the trap. Good luck, tom