We can only speculate but I would say that it is unlikely. George R.R.Martin has said that he does not like the idea of bringing people back to life better than before. He wants them to be alittle worse for wear.
If what the Red Priests say can be trusted, a fire burns inside everyone that gives them life. When they die the fire goes out. When Red Priests bring people back to life, all they are doing is reigniting the flame of life within them, it's not something the resurrected person didn't have before. When we see Thoros of Myr praying over Beric Dondarrion's body, he says "His flame has been exstinguished, restore it." If anything the flame of life would be burning lower than before, making Jon more susceptible to the White Walker, if that's even possible. So the simple answer is no. Jon has not gained anything from his experience, his inner fire was always there and we have seen that it doesn't protect other people from the White Walkers. Jon's inner flame is likely even weaker than it was before.