Bilge pumps are high volume, low pressure in the 30-50psi range. With a 1/8” coolant nozzle I doubt it’s using 10% of the pump’s capacity. In fact, if it weren’t using a bypass line you’d probably wear it out prematurely. I have a 1/2HP bilge pump that warns to use 3/4” hose minimum. That size hose flows 4X that of a MR-1 3/8” coolant line.
Couldn’t hurt to try it but I think peck drilling would work better. I looked into flow through coolant systems a while ago and found they use 10-20 times more pump pressure.