The bypass is sized so that can't happen.
Funny story:
A buddy of mine's dad had a 2-bolt roller SBC built for his S10, they went with stock clearances but of course he had to have them toss in that HV oil pump. Relief pressure on that pump was 55psi IIRC and it would produce well north of 60 on a cold start with 15w-40 in it, clearly overwhelming both flow through the engine and the relief. If you drove it you could get upwards of 90psi IIRC. Once warmed up and thinned down idle pressure was around 40 and you were on the relief again by 2,000RPM. Just a complete waste, that engine would have been fine on an SV pump.
It would toss massive amounts of oil out the pushrods when cold (I remember crisp fall starts getting ready to take it to the track and having a valve cover off checking rocker lash) while of course sitting there with the relief wide open.
Ford had an issue with the 4.6L IIRC where the relief on the pump would stick and the oil filters would balloon, though I expect you could achieve the same by seriously overwhelming the bypass and increasing system pressure to something obscene.