The rules would seem to suggest he can be signed outside of the window (57.2 below).
57.5 as it reads could also be interpreted as suggesting that they could not claim compensation if the player is no longer under 24.
57 Registration of Non‑contract Players
57.1 The registration of a Non‑Contract Player will be valid only for the Season in which the registration form is signed.
57.2 A Club may only register a Non-Contract Player (subject to the provisions of Regulation 41.7) during a Closed Period if he is an Unemployed Player.
57.3 A Non-Contract Player's registration will expire at the end of the Season which for the purposes of this Regulation, will be deemed to be the third Saturday in May or within four days of the Club's last match of the Season, whichever is the later. After this date the Player may sign for another Club for the following Season or he may choose to re-sign for his former Club.
57.4 A Club wishing to immediately re-sign a Non-Contract Player should include his name on its Club List of Players for the following Season and notify the Player of its intentions in accordance with the procedure laid down in Regulation 67.
57.5 A Club will only be entitled to seek a Compensation Fee for the loss of a Non‑Contract Player's Registration who is an Under 24 Player if such Club has made the Player a written offer of terms to become a Contract Player prior to the expiration of the Registration or for other reasons satisfactory to the Board. The amount of such Compensation Fee shall be agreed between the two Clubs concerned or in default of such agreement should be determined by the Professional Football Compensation Committee on the application of either of such Clubs.
Read more at
http://www.efl.com/global/section6.aspx#BUGeOgYT5cSKgmc5.99