Will the starter relay on a 1993 ford Taurus 3.0 cause vehicle not to start?

Yes, a faulty starter relay on a 1993 Ford Taurus 3.0L can absolutely prevent the vehicle from starting. The starter relay acts as a switch, completing the high-current circuit needed to power the starter motor. If the relay is bad (stuck open, internally shorted, or burned out), it won't close the circuit, and the starter won't engage.