is it safe to say that they will last barring any unavoidable things that are out of my control? Seller asking $3,700?
1 thing you have to keep in mind is that out of all of the possible propulsions methods for boat, and by that I mean, Inboard, Outboard, Sterndrive and Jetdrive. Sterndrive is by far the most amount of maintainence. If maitainence is lacking, then overdue items is going to catch up with you real quickly. But if the seller has records, and everything has been kept up according to schedule, then your okay.
As far as 3700 goes.... Well. Good used boats are hard to come by (good ones in good shape with all records). So in that respect, they usually sell for higher than book value. NADA values the boat at 1600 in running condition.
If this boat has records, if you can water test it, and the boat makes full power and has no problems. If it is in good shape with a clean interior and decent gel coat, and the trailer is in good shape, without seeing it would say no more than 3. (that's almost twice NADA).
But if there are no records, if there are issues, if it needs work. Then your looking at book value or less. Personally I would never buy a boat I could not water test. Aside from making full power under load, you have to make sure the thing doesn't leak. And if you can not water test the boat, personally I would pass.
Just to give you an idea, if this needs some overdue maintainence items like the bellows, shift cable, gimbal bearing, oil changes... that will all run you 1k + on top of whatever you pay for it. So records are key. Does that make sense?