As in your other thread.....
Yes... the cavitation can be bad enough to overheat the engine. BUT... the boat would never break 10 mph or so.
BUT......
If your buzzer is working, and your temp sender is good...... AND... you know that water is flowing though the pee-hole.... then NO... it would not get hot enough to damage your oil drive gear.
With that said.... the engine could have been overheated, and the gear could have been damaged before you ever got the boat.
Since your engine is apart... look at the pump shaft, and see if it's discolored, or scarred at all.
Finally.... did you test the temp sender, and buzzer to know if it's working? Also... the Merc powered Islandia has 2 buzzers. (bet you didn't know that) The reason is... it's a mix of seadoo and Merc electronics. On my 2002... the "Seadoo" buzzer was bad. AND... that's the one that gives you the temp warning.