No, Scouse is an accent which can be both sides of the water. A Scouser is a person from Liverpool. I lived there 14 years and never heard anyone from 'over the water' describe themselves as a Scouser. The people of Liverpool also do not regard those on the other side as the same. Merseyside is an execrable county that should be binned, Liverpool is Lancashire and the Wirral is Cheshire.
