No, the alarm continues to go off whether the motor is running or not. Here are the pictures showing the 2 lights that are lighting up on the alarm module.
I recently purchased a 1995 225 Mariner outboard. When turning on the key, alarm begins to beep and light up the oil and tempature light back and forth and continues to go off the entire time boat key is switched on and running. Motor runs great. I have had it at two different boat shops in town...