Yes it is I've done it. It's my local network as well. You can do the Wirral line starting at Liverpool then going to either New Brighton or West Kirby, then back to Hamilton Square to do the other, then back again to either Chester or Ellesmere Port then change at Hooton to do the other then back up to Liverpool and do Southport first, then back to Sanhills and then Ormskirk and Kirkby then finish off at Hunts Cross.
Ticket-wise you will require either a Merseyrail Day Saver or a Saveaway. The Day Saver is available from Merseyrail TVM's and ticket offices but also anywhere else if 'Chester' is put as the FROM station and 'NORTHWIRRALLINES" is put as the DESTINATION station. It is £2.35 Child and £4.70 adult. It allows travel on both Northern and Wirral lines unlimited after 09:30 and all day Weekends. This is issued as a single ticket but don't be confused by this, it just works like a rail ranger. It always confuses people!
The much better option for better value is the Saveaway which can only be brought from ticket offices and guards using the code 'MTE'. It allows travel in a much broader zone but with buses and ferry also. It is priced at £2.50 Child and £4.80 adult. This is issued as a rail ranger ticket.
Here is the validity area for the Saveaway.