To the main topic, no. It's not possible for Crono to be dreaming. One, It's too long to be a dream. Two, Crono is woken up by a guard and told his execution was cancelled (which was in the dream. WTF?) and of course, there's the whole Epoch to dismantle, Crono's mom being sucked through time, and all those biznatches from the dream dancing at the fair. W.T.F?
Not to mention that Crono is dead for a good portion of the game, and all the personalities and events are simply too complicated for a sedated (basically) barely conscious mind to understand and create.
Not to mention that whollllle game of Chrono Cross. Wow. Doreen says her quote because, being a Dream of Melchior's, she was probably recently created and pondering her own existence. Masamune means Grandleon, and Mastermune means....Masterleon >_>;;