Yes, but you have to be careful. Most mortgages have a due-on-sale clause that allows them to foreclose if they did not consent to the change in title. There usually is no problem getting that consent with a provision that you are still personally liable on the loan.
The transfer would protect you as long as there is no pending litigation and assuming the transfer is not to avoid an existing liability.
If properly done, a creditor of the LLC would only be able to go after assets belonging to the LLC.