Personal view... YES! before a ticket is issued a valid rod license should be produced. Clubs and syndicates should do it too. A very complex system would be required for the online purchases though, some form of verification with the EA database.
Problem is it creates more hassle than its worth. You'd lose money, have to chuck someone off the fishery which could result in aggro. An EA officer was assaulted recently http://www.anglersmail.co.uk/news/rod-licence-dodger-guilty-of-assault-74962
A responsible fishery owner would check, one that cares about the industry/environment/etc. unfortunately many are only in it for the money and dont actually care beyond growing the bank balance.