Definitely NO, if I had to pay to play online I would not buy the game.
There is absolutely nothing that justifies an extra monthly fee, since diablo 3 IS NOT an MMO.
In MMOs, there is always extra content being implemented in the game, which justifies the monthly charge.
Diablo 3 is supposed to have "fixed" content. The maintenance of the battle.net servers is just a cost that comes along with the offering of the battle.net service, and should not be re-transfered to the players.
-Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy's First Law of Equivalent Exchange. In those days, we really believed that to be the world's one, and only, truth.