No.

Mickey saves you (mostly) up to some of the battles until you meet him again at Hollow Bastion (Space Paranoids mission). After that, Mickey only helps you in specific battles, (and very few I might add), most notably, Xaldin. He BEGINS saving you when you and he meet before heading Yen Sid's Tower.

He doesn't save you at any point during Timeless River, Pride Lands, Halloween Town, Disney Castle, Hollow Bastion, or Twilight Town. He also does not save you when he is traveling with Sora, or when his location is known.

To get Mickey, you must die in a boss battle. Assuming you are given a choice, choosing "I won't give up!" will allow you to continue. Mickey cannot kill a boss, and you automatically revive if he is killed. The chances of Mickey arriving are based on how many times you have continued (this means died, and chose Continue).