Disagree. Gandalf was Maia, and was therefore immortal. Being immortal didn't preclude him from being killed however, as was also true of the elves.
The fear of men, however, leave the world upon the death of their bodies. They cannot be rehoused within Arda without special permission from Eru. That's exactly what happened to Gandalf the Grey when he died, therefore he was mortal. The fact that he was sent back into Arda by Eru until his task was completed further suggests that, after the War of the Ring, Gandalf the White fully expected to die and leave Arda again. Makes the Valarin debates over which Maia gofer should be sent into Endor take on a rather macabre tone.