Fingers crossed for you. Do yourself a favor and check the shaft log for cracks where it exits the hull. If they torqued it good you might see some evidence of damage. The problem you will have is that you have no history with the boat. What is it powered by? A 1977 might have an A4, but if it is a 2 cyl diesel they vibrate a lot anyway.
At the advice of a surveyor and hired Captain I did the whole shaft, coupling, alignment thing if you need some advice next year. When I bought my boat because the surveyor said the alignment through the cutless bearing was off and the bearing needed replacing. First thing I did when I got the boat. What a PITA. It was three hours from my house, during a hot stretch and the damn prop wouldn't come off for love or money. I broke two prop pullers. The PO said it was fine and I should have waited a season for sure.
My firm advice is to run it an see how it behaves. Don't go looking for trouble. If the strap was less than six inches out on the shaft it is probably fine. Just print out the picture I sent you and have them do it that way in the future.