I was wrong. Players of clubs who finish 1st, 2nd or 4th in the CL groups can play for a different club in the EL in the same season.
So yeah, he would be able to play.
Further, as per Champions League regulation 17.18, one player per club who would normally be cup-tied can be registered and eligible to play, so long as his previous club did not field him in the same competition, meaning that this player can represent two different clubs in the Europa League and Champions League. However, if the first club fielded him in the Champions League, but would later play in the Europa League through finishing third in the group stage, the transferred player is ineligible to play in the Europa League. This was the case with Alan Hutton who could not play in Europe for Tottenham Hotspur following his former club Rangers' entry into the cup.[2] However, if Rangers had come 1st, 2nd or 4th in their group, Hutton would have been able to play for Tottenham.[2] Another interesting case came in 2009, when Real Madrid purchased both Klaas-Jan Huntelaar and Lassana Diarra – both of whom had already played European football during the season for Ajax and Portsmouth respectively – during the winter transfer window. Because of UEFA rules, Madrid had to pick one player via regulation 17.18, and ended up selecting Diarra for their European roster.