Just to be clear, the YouTube link is a trailer for a theatre tour, next year, by two actors doing a stage version of 'The Navy Lark'.
Seems a popular thing, in that a version of the 'Dads Army' radio show was recently touring theatres in England, this year, with two (different) actors doing a show based upon a mish-mash of material from several episodes of the 1970s 'Dads Army' radio show. One of the two was David Benson, who began as a Kenneth Williams impersonator, on stage, and also does Frankie Howerd. He was on tv as Noel Coward in 'Goodnight Sweetheart'. A guy with that sort of talent - I saw the shows, even talked to him about Williams - made the whole thing a success.
I think it depends on the individual actor, whether he can get away with impersonating a half a dozen famous stars in one show. Benson did! He had a Hollywood party sketch, in his one-man show, where he jumped from Cagney to Bogart to Sinatra to Coward -- and to Judy Garland! And made it look effortless.