Usually not the way the powertrain warranty reads. Generally means anything that touches oil is covered, not electrical. Emissions might be a better route but have to identify the problem first and see if it can relate to an emissions item like ECM or something.
You know I really think it is time to take it to a dealer. I had a balancer problem with my Buick which was slightly beyond the warranty and the dealer covered it through goodwill.
One possibility is a portion of the starter armature is damaged, and not making good contact with the stator. Sort of like the Wheel of Fortune. If it happens to stop in a good area, it will start the next time. If it happens to stop in a bad area, it wonāt. There are many other reasons for this sort of behavior, but thatās one of them. And easy to understand b/c most everyone has seen the Wheel of Fortune.
It seems to me there has been some bad guessing going on; especially with the fuel pump scenario. And then to claim the new fuel pump was also faulty just makes it look even worse. The odds of a 50k miles Honda starter or fuel pump X 2 being bad in the first place are as close to zero as it gets IMO.
Without car in hand about all I can suggest is to have someone probe the small starter solenoid wire with a test light or volt meter and work the key repeatedly with the fuel pump fuse or relay removed.
That would keep it from starting but would not affect the starter motor operation. If during the testing the test light or volt meter is inoperative that means the issue is related to the ignition switch or neutral safety switch. Tend to lean to the latter.