Here's my take on the question:
It depends entirely how much piston to bore clearance you have. and the expansion rate off the alloy in the pistons. Do you mean due to heat or the lack of oil?
Heat wise,
A worn motor will go longer than a new tight one.
No one would have done tests for this.
If you have solid skirt pistons or split skirt pistons changes it.
Many things will come into it.
Racing clearances are much bigger than street clearances.
Engines are built for specific applications. The flathead was first built for a no pressure cooling system, which means she boils at 212 degrees at sea level.
If you want one to run at 260 degrees with a 14 pound pressure cooling system then you would adjust you assembly tolerences to suit.
It is hard to answer your question. It is about as vague as trying to say "how long will it go before locking up" Depending on the surrounding circumstances, a long time, or no time at all.
With a lack of oil it changes. Here the rings will likely grab first, no load, idling a long time. Under load,high revs, about 1 turn of the crank.
Here is an example of a sort;
My son in law works for a firm that hires generators. (diesel)
They don't sell them, they scrap them, when they are finished with them.
They removed the radiator, and dropped the oil from the sump of one a couple of weeks ago and left it idling. Apparently it idled for a couple of hours. Not bad I thought.
Does that help?