I second what shoe box jack said. If you are aware of this possibility it can help but the only electric pump I have is on my avatar roadster and it has been pushing fuel just fine for 21 years now. No stock pump in the equation. All my other 4 flathead only use the stock pump.
Back when I was a teen, I put a flathead in my first car, a model A. I figured who needs a fuel pump, when gravity will do the job. Well, after not shutting off the fuel valve the night before, it wouldn't turn over to start. When I looked at different parts of the engine I noticed gas coming out of the dipstick tube. Hmmmm. Shut the valve off, drained the pan, got the crap out of the needle valves of the 2 97s and all was good.
A ruptured diaphragm (while rare) could give you the same problem but while the engine is running and the result could be catastrophic. My MISC album has pictures of a friend's car that the gas tank filler neck was torn off by a chunk of an old tire that blew. Rare event but catastrophic result.