After the repair, if your existing insurance company has any reluctance to fully insure the boat (I wouldn't blame them...), get a clean survey and switch to another company. Does your state even have titles for boats...many don't...
This advice smacks of fraud, and
if it is in fact a CTL, and you repair it and offer it for sale or transfer - you will be in deep doo doo. Subject to prosecution in many states. If you are going to go this route, I suggest strongly that you READ the terms and conditions that you agree to, by taking the check.
For sure you can repair it and use it....but if involved in an accident, that can in any way be attributed to the CTL damages, you can and likely, will be find liable...and without insurance.
The HIN, make, model and ANY information they have on the boat and you will be entered in to the databases available to the insurance companies and made available to other insurance companies.
Whether car/truck/boat/motorcycle.....you WILL have a next to impossible time EVER insuring that boat again. Insurance companies will NOT pay twice. Once totaled, they - collectively are done with that item. To them it no longer exists, and their lawyers are better paid than yours will be.