They can play. They are on a season long loan.
FA CUP RULE 15
(j) Temporary (loan) Transfers
• (i) A player on a temporary (loan) transfer is ineligible to compete in the Challenge Cup Competition unless permission to do so is given by the lending Club in writing and a copy is received by The Association by 12 noon on the Friday prior to the date fixed for playing the Round. Any permissions must clearly state that the player has approval to play in The FA Challenge Cup Competition. A registered Trainee or a player who is registered on a Scholarship for work experience may play for another Club, subject to written permission being given by the Club that he is registered to and provided that such permission is received by The Association by 12 noon on the Friday prior to the date fixed for playing the Round. The Association will not give permission for players on loan or work experience to play against the lending Club.
• (ii) A player recalled, at any time prior to the date of the Round, to his original Club from temporary (loan) transfer, in accordance with the terms of the loan agreement, may represent his original Club. Such player may only play in postponed and replayed matches if he had been recalled in time for the first match in accordance with subparagraph (i) above and (iii) below as applicable.
• (iii) A player on temporary (loan) transfer is eligible to compete if transferred by the lending Club to the loaning Club after the date and time for player qualification for a round but must have been eligible to play in the original tie.
• (iv) Players on season “long term loan agreements”, are not considered “loan” players for the purposes of the Rule, and are therefore eligible to play in the Competition.