Scotty, that depends on the extent of pump failure. With total failure, you are correct of course.
I have seen hydrostats barely creep along with a compromised pump. If I read correctly, his tractor moves if it’s down hill then it stops or something to that effect. Replacing these pumps brought the tractor back to life.
Now this is with my brand and granted am unfamiliar with set ups in other brands meaning if there are safety valves that engage with a sensor solenoid or relay so a tractor doesn’t blow its pump upon a fluid distress situation.
At any rate, l hope the op all the luck in the world to find the solve to this problem inexpensively with the leak in his suction tube perhaps being a main culprit.