As posted earlier the answer is not and not, but before we get carried away with proposing alternatives, let us remember as far as I know the 507 & 508's are full size stock, and height wise are identical to the 313's.Wikipedia states on the record for 508's
"The class was developed for Merseyside following extensive trials and testing of the 4Pep/2Pep stock built in the early 1970s. Testing of Class 313 took place on the Northern Line on Merseyside, using 313003/005/013/063 loaned from the Great Northern Line of the Eastern Region to Hall Road depot."
One assumes this testing used the third rail capability of the 313's whilst the units were still fitted with pans, and that the Wirral Loop tunnel is the same diameter as the Northern Line terminal. Therefore, the one unanswered question is whether there is sufficient clearance for a working pan, and that is something I cannot answer, but in a worst case scenario if the new stock and/or replacement stock is dual voltage there would appear to be no major reason why the third rail could not be retained within the tunnels and approaches.