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As long as they do not interact with any other particles then yes.
Remember, in the photon's frame of reference (i.e. It's point of view), time does not progress. So it is created and destroyed in the same moment. Any distance traveled for any amount of time in our reference frame, happens instantaneously for the photon.
Couldn't the same be said about black holes/singularities?
Yet they will evaporate via Hawking Radiation, over the course of eons upon eons of time.
There are no valid inertial frames for an object moving at the speed of light. The idea that “a photon doesn’t experience time” is a common, but misleadingly incorrect statement, since we can’t define a reference frame for it. Sometimes this misconception can be useful for conveying some qualitative ideas (photons don’t decay), but often it leads to contradictions like your question about Hawking Radiation for black holes.
Man, that is one weird concept to wrap one's head around. In fact, I'm not even sure what it means, how to visualize it, my mind trying to "make out the gears that make the contraption work", how do I make it let go of the classical physics it clings to?