If the boat is going to the hill, pull it all out, realign/true the shaft, and spin the wheel as well. A proper prop shop, (liked that didn't ya?), will computer balance it along with the shaft, WITH a new coupling on it. You may salvage the old coupling, but I end up more often than not cutting them off.
So yes. Or no, whatever. Anytime the coupling has been split, always check your alignment. The motor will settle on the mounts, maybe just settle in on one side or the other, or something. I have never once put a shaft in that lined up right. This is TOO easy to check. A feeler gauge between the coupler is about it. I shoot for under three thousandths of an inch, but I think the criteria is five. Close enough. And yes, a dial indicator with a heavy base can tell you if it has problems, but it's really unnecessary.
If the shaft is not bent all to hell, or the wheel has a shark bite out of it, the shop can generally re-true it all. The last one of these I did a couple of months ago I think was somewhere around two hundred bucks. New Buck cutlass bearing and shaft coupling, set screws, and shear pin realign the shaft and prop. That's cheap insurance.
And I have a FIRM policy of what needs to transpire on the hill. Underwater issues are dealt with closely. With extreme prejudice. It's underwater. Around here, a haul, block, and launch on a thirty footer is about 300 bucks. I want it fixed right the first time. And yes, I have re-hauled them twice, and one time three times. On my dime. It has to be right.
People can deal with an alternator or winch while afloat. Maybe even underway. I don't need to get into the hand wringing about when underwater issues occur. You KNOW when. And it's never in crystal clear water in the islands, sun out beautiful, wife happy, no traffic, every tool you need on board, etc...