I am sure they do but you would have to diclose that to your mortgage lenders as for example, they might not be able to obtain vacant possession were you to default on the mortgage
Yes I've done it, but as FTVS says, it is highly likely that under the terms of your mortgage agreement, you will need to obtain your mortgage lender's consent.
without your mortgage lenders consent if they find out they can go for possesion or complete repayment as you have broken the terms of the agreement and if your buildings insurance is with them there is a good chance that it will not be covering you anymore