Technically, no, but they both debuted with the team in 1993, following the 1992 NFL Regular Season:
In January '93, Bill Parcells was hired as coach of the New England Patriots.
In April '93, Bill Parcells selected Drew Bledsoe in the NFL Draft.
In September '93, Bill Parcells coached his first regular season game with the Patriots, while Drew Bledsoe started his first regular season game with the Patriots (and in the NFL).
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