Welcome to the forum, it doesn't work that way. If there is an oil pressure switch in the fuel pump circuit, it is wired in parallel to the fuel pump relay. As long as it wired in parallel the o/p switch can't keep the vehicle from starting or kill it, as long as the fuel pump relay is functional. Now, if the o/p switch is wired in series to the fuel pump, yes it can kill the engine.
If there is no oil pressure, the engine may sieze, it will kill the engine and it won't crank if it is siezed.
Which cutlass is it? There are usually several listed.
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Sunday, February 21st, 2010 AT 2:25 PM