Yes, it might, rather depends whether the roots are still active or not. You don't say where you are, but if you're in the mild west or south, cut down now - if you're north or midlands, wait a week or two and do it then.
In future, don't use bubblewrap to protect it - use horticultural fleece, and always remove the wrappings when the weather in winter is mild - you only need to have it wrapped properly when the temperature falls to 4 degrees and below.

bubble wrap is best for rapping plant pots as aposed to plants as they cant breath and they sweat inside it .