Yes if the fuel shut off solenoid gets fried the engine will not start.
But to back feed to the fuel shut off solenoid the plunger in starter solenoid has to be stuck. In our trucks this usually caused by worn contacts (especially battery side) and the starter stays engaged (running) until plunger is disengaged.
If your stater is not running when engine won't turn off then the contacts are not your problem but it is a good idea to upgrade to better ones.
But to back feed to the fuel shut off solenoid the plunger in starter solenoid has to be stuck. In our trucks this usually caused by worn contacts (especially battery side) and the starter stays engaged (running) until plunger is disengaged.
If your stater is not running when engine won't turn off then the contacts are not your problem but it is a good idea to upgrade to better ones.