Oh they will start they just wont RUN - solenoid will only close off the main emulsion tube, fuel will still be fed through idle circuitry but at WOT position the engine will be excessively lean - after enough cranking you may have enough fuel vapor to start a slow combustion that may still be burning slightly when intake valve is open.
Have had it happen before on a Briggs engine - no start just backfires, the fuel solenoid circuit was not grounded (someone did not hook up the ground wire)
Took the shade tree guy 2 days and several "Try it and see if it fixes it" parts (Coil, 2 new plugs, valve job, to name a few things he did) before giving up and it came to me - while checking it over I noticed the solenoid ground hanging loose, hooked it up and she started right up just fine - had to do a little bit of adjustment work and re-work of the other guy's "fixing" afterwards..