Hi William,
I love to test and research things and this just happened to be one of them. My test was strictly that, a research test and not for any operations. Just something I wanted to know. Inquiring minds wanted to know. LOL
This test was done with a Flight Design CTSW high wing.
I did a research test years ago about this very thing. Of course Rotax says 2.2 psi, but I wanted t know how low a pressure would really work. This only works with a high wings because of gravity. Low wings must have an electric pump back up and even high wings should.
So I pulled the inlet hose off the pump and the outlet hose. I took a metal tube and connected the two hoses. So now the fuel was only gravity fed. I ran the engine up to full throttle and it never coughed or sputtered. Then I thought this wasn't very realistic. So I replaced the hoses on the pump and removed the pump and just let it hang there basically totally dead. Then I put a blind over the open hole on the gearbox so it wouldn't lose pressure or oil. So when a pump fails it fails open. I ran the engine again and I could get up around 5K rpm, but any more than that the engine did sputter from lack of fuel. This was only gravity fed pressure.
So to answer your question will the engine run if the pump fails,,, yes, but it would be extraordinarily rare that such an event would ever happen. Pump diaphragms can leak if it's getting too worn or old, but totally failure probably isn't in your future.
MFG's put limit specs on many things to keep whatever someone is using in a safe zone and so people won't push the limits and get in trouble or get hurt. Liability for MFG's is in play too.
So even though I might test something I still stay within a MFG's published limits when using their equipment. It's for the product longevity and safety that we should stay within any MFG's specs during usage.