@hikermor nailed it - only you can decide.
But, if I were in the same position, I'd be thinking that I don't know what will happen five years from now after I am done my PhD. Maybe I'd be in a position to do the PCT and maybe I wouldn't be. So, adhering to the principle of "I'd rather have memories than dreams", I'd go for it.
I would decide quickly, though. There's a lot of preparation needed if you're going to hit the trail in a couple months.
“Between every two pine trees there is a door leading to a new way of life.” (John Muir)
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