No. That wasn't Gandalf's gift. But I think that Aragorn as King is more a throwback to legend and perhaps to some pre-Christian and post-Christian views that the king is viewed as a healer just as the King of kings (Christ) is not merely a saviour, but able to heal all sickness and woe. Medieval literature often displays kings in this way. But Tolkien is careful not to make Aragorn into a Christ figure. Aragorn is not perfect. Tolkien just uses some very familiar archetypes that are embodied in Aragorn as the benign and just king.

I don't recall reading in the Bible where an angel ever healed anyone, and if we assume that Gandalf is a sort of angelic being, then it fits in with Tolkien's religious views.