Logic indicates that the question "Is X a Premier League player" is an easy one.

If they are on the books of a Prem League club and eligible to play in the Prem League for that club, then yes they are a Prem League player.

If the question is intended to instead question if the player is of Premier League quality, then it's impossible to give a definitive answer. There's no objective "Premier League" standard, opinions of players abilities are subjective and players of all quality levels have played in the Prem League, including someone purporting to be the cousin of George Weah.