Doubtful, not impossible, but doubtful. The more common trucks that would lose oil pressure on the gauge were the early build trucks 03-04, with the cast iron pump cover. there was a check ball on the feed side of the pump that would fall out and cause a MASSIVE low pressure system oil leak the LPOP couldn't keep up with.
What I would do first, is check the base engine oil pressure with a mechanical gauge, to rule out a sender/wiring/cluster issue.
After you've done that, report back.
The gauge in the dash measures the oil pressure in the low pressure system, not the high pressure system.
If your truck loses HP oil for any reason, you will likely experience rough run/stalling issues.
Hope this helps. I've changed a LOT of oil pressure sensors on these engines for this exact issue. Unhook the connector at the oil pressure sensor on the top of the oil cooler (single wire) and see if it's leaking oil into the connector as well.