no, because the window circuit is not [or shouldn't be] tied into the starter circuit to the starter relay. the reason for this is all circuits other than the starter and ignition system are disabled on "start" to allow all available battery voltage and amperage to be used to get the vehicle running. however, you need to have power from the "run" circuit to power the window circuit when the car is running. many times i have seen, and repaired, the window wiring at the door junction due to frayed and broken wires. sometimes there is just enough "connection" at those wires to make the window work, then with the engine running, the vibration[s] is enough to open the broken wire strands just enough the window won't then work. i would start at the ignition switch and work toward the window switches. could also be a bad master switch or the connection to it at the drivers door. a FSM would be a good idea, as it will guide you step by step in the electrical section to diagnose your window problem. wiring problems can sometimes make a guy pull his hair out [that's why i don't have much on top anymore], but if you take your time and think a little, all those bad boys can be fixed. the intermittent ones are the worst though, to solve. keep us informed on your progress and don't be afraid to ask more questions even if you are discouraged by some grumps on here. i'm more than happy to share my experiences before i croak.