Unfortunately, no, it doesn't die. "Dies" has a specific meaning:
700.4. The term dies means “is put into a graveyard from the battlefield.”
The token does cease to exist once in the player's hand, but that's due to other rules, and that's not considered dying either:
110.5f A token that’s phased out, or that’s in a zone other than the battlefield, ceases to exist. This is a state-based action; see rule 704. (Note that if a token changes zones, applicable triggered abilities will trigger before the token ceases to exist.)
But, this has an interesting implication that a token can die and is temporarily in the graveyard, thus satisfying death triggers.