My carrier was fine with it and the only change that was needed was to identify it to my mortgage company. Rate remained the same and all is good.
If you are putting your home in a trust to battle the banks that's not a bad idea, however, it's a long drawn out process and no guarantee. However, you may want to consider a strategic short sale and have the bank pay you to move and have your debt forgiven.
If you'd like to speak more about it. I'm here to help, no obligation counseling.
Lic Re Broker