desmond in the FST (dead or alive)

was desmond dead like everyone else during the entire FST?

or did he time-travel to the FST while he still was alive in OT?

-him randomly appearing on the plane makes me think he was "time"traveling -but him being in the church at the end makes me think he was dead at that point -im half tempted to think he travelled to the fst bc he chose that over the ot -what about during happily ever after, was he jumping then?

im confused can someone help straighten me out!

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