Proper fans certainly do realise it. Those who think tennis takes place two weeks a year probably not. I used to say to people who mocked Tim Henman as a loser that we should enjoy having a contender because another won't come along for a long time. I was proved wrong with Murray coming along, so hopefully there'll be someone to follow him.
Thing with Henman was Rusedski came along a couple of years earlier (as in made the big breakthrough first, Tim made the 2nd week of Wimbledon before Greg did) and caught the imagination. Big serves, Grand Slam Finals, he had the game that Mr Dependable/Boring Henman didn't. By the time Henman did reach a final (Indian Wells) or win a masters (Paris), Rusedski had already done both at the same venues - not that the general public really knew much about these tournaments as they do today, mainly because Murray's success makes the Masters series get more column inches.
Agree with the Murray sentiments though, clearly one of the greatest British players ever (thats including Perry, Austin et al). However I don't jump on the 'Could've won more in another era' bandwagon. Each decade seems to have its 2, maybe 3, huge dominant names.
00's - Federer/Nadal
90's - Becker/Edberg, then Sampras (mid-late 90's probably could've done with another challenger really)
80's - McEnroe/Lendl
70's - Bjorg/Connors
60's - Emerson/Laver (and the rest lost to the Pro ranks)
etc etc.
Think its a big jump in faith to say Murray would automatically sit at home with those players, maybe coming along 10 years earlier might've seen him win a few more (the gap between Sampras retiring and Federer starting to dominate, only 3-4 years but still). However, even winning two majors is a fantastic achievement (add to that Olympic gold too)