Centaurus has asked an odd question, and then gone on to cloud the issue with an even odder comment (IMHO)!
I don't agree that operating the primer as part of your investigation into the cause of the failure is a reasonable thing to do. As Tinstaafl says, operating the primer is likely to lead to the engine STOPPING, not causing it to burst back into life following a mysterious stoppage. If fuel starvation was the cause of the stoppage, I think it highly unlikely to primer could suck any fuel in (where would it suck it from) - and if it did manage to suck in some fuel, so what - the only impact would be to supply a drop of fuel to an engine that has stopped because it has run out. If you operate the primer quickly while the engine is still coughing and spluttering it, will just cough and splutter some more and die about one turn of the crankshaft after it would have died if you had not operated the primer. So no gain there, and if you operate the primer after the engine has died, you just get a primed engine. The action would not, in my opinion assist with the fault diagnosis.
Centaurus' odder comment was that use of the primer help, or indeed be needed to, re-start an engine after it had stopped. I think this very unlikely unless you have spent ages descending and the engine had got cold like wot it is in the morning.