Can a metal halide light that has to have a 20 amp circute to run on start up with a 15 apm timer

It will start and run on your timer, but I can in no way suggest you do that. Your timer will be overloaded and be a fire hazzard. I strongly advise you get a timer with the proper amperage rating.

If you mean the timer is only rated for 15 amps then the answer is no.

It would depend on what the "inrush" current would be.

Also, if the light truly requires a 20 amp circuit, then you need to remove the 15 amp timer because it may burn up on 20 amps.

Normally, I would expect that the 20 amp circuit requirement is because there is an inrush current greater than 15 amps when the lamp is turned on. After the start-up, the current drops off.

What is the wattage of your metal halide light? A 400 watt metal halide light powered at 120volts only pulls 4 amps.