LLigetfa
DIYer, not in the trades
That should work but I would advise to use a reverse pressure switch, not a conventional switch with low-cutoff as they need to be manually reset when they trip.You could also put a low pressure cut off on the suction side of the jet pump.
Also, I would use it in conjunction with a CSV so that the pump doesn't run at max GPM while refilling the pressure tank. If the pump is let to run flat out, it will not only pump as much as is being drawn but will also see the pressure tank as additional draw.
Many folks don't quite understand that low pressure is often a side effect of low flow so trying to increase the flow will lower the pressure on the pump inlet to below zero. In the OP's case with the leak, much of the flow is robbed by the leak so it really is a flow problem, presenting as a pressure problem.