Yes. A player can only be excluded from the FA cup if they have already played in the cup as a member of 2 other teams or if they have a suspension.
Birmingham
Chelsea, they beat Portsmouth 1-0, completing the League and FA Cup double.
The 1970 winner of the FA Cup was the Chelsea Football Club.
Chelsea football club was the winner of the FA Cup in 1997.
was the winner of the 2000 FA Cup was Chelsea football club.
Chelsea football club was the winner of the FA Cup in 2007.
Chelsea football club was the winner of the FA Cup in 2009.
The winner of the 2009 FA Cup was Chelsea Football Club.
Chelsea Football Club was the winner of the FA Cup in 2010.
Chelsea football club was the winner of the FA Cup in 2012.
The winners of the English FA Cup in 1970 were Chelsea.
The winners of the English FA Cup in 1997 were Chelsea.