Since there is a lien on your vehicle, hell yes the insurance company would let them know. The lienholder gets a copy of your policy, plus any changes you make to it.
The big question is what does your loan contract say? Registering a lien on a vehicle doesn't automatically give the lender the right to insist that you carry Collision coverage, that has to be spelled out as a condition in the contract. Unless the contract says you agree to carry specific insurance coverage (like Collision, for example) until the loan is paid off, the lender can't make you buy any insurance at all.
Since the contract probably does say you agreed to carry Collision coverage (they rarely forget to put that condition in), what you want to do is ask your lender. And ask them before you make any changes to your coverage, not after they get a copy of your policy and call you.
If you ask in advance, they might just say no problem. I've gone without Collision coverage on financed vehicles before, and my lender had no problem with it. Because I asked in advance and the vehicle was going into storage.