Hello and welcome Ferd01. The answer is, "yes, if you're lucky". I would leave them be for now, then cut off the trunk below any soft, rotten areas and hope that it regrows with offshoots from below. The chances are reasonably high that it will regrow. I wouldn't do it just yet, as pruning will prompt the plant to start growing, and I think we have more cold, possibly freezing, weather to come this winter.

You will almost certainly get regrowth from the base of the plant, so as Beattie says, leave it for now. From the end of March I'd remove any remaining dead leaves by hand.