The issue at stake in the Tevez affair was that the third party had the right to sell Tevez. I'm fairly sure that this extened to a right to prevent him from playing on a game-by-game basis, although I can't remember whether this was in the contract or simply the reality of Tevez's relationship with MSI. That's not what we're talking about here.
From an FA perspective the Tevez affair isn't really relevent. The football club selling/loaning a player is not a third party to the contract, they're one of the two parties engaged in it and the rules on third party ownership have nothing to do with such arrangements. In fact, slightly confusingly, the FA define third parties as "
a person or entity that is not a Club or an Overseas Club." which seems to suggest that there's nothing in the FA's rules on third party investment which precludes a third club from having an interest in a player. More on that in a bit.
Moving on from third parties, can no-play arrangements exist between clubs? Certainly not in UEFA competitions (which we should remember for a few years' time when we're in the Champions League):
"any provision in a private contract between clubs which might function in such a way as to influence who a club fields in a match is null, void and unenforceable so far as UEFA is concerned". This was clarified in the wake of the Courtois incident last year where it was claimed that Athletico were obliged to pay Chelsea extra money if they wanted to play him against his parent club.
Conversely, in the Premier League, a player on loan is explicitly prevented from appearing against his parent club (
V.7.2. during the period of the Temporary Transfer of his contract registration a Player shall not play against the Transferor Club
- partly to avoid such allegations of impropriety. Not so in the Football League where this is the default position but the clubs have leeway to explicitly allow the player to appear (
52.5 During the period of any temporary loan transfer, a Player shall not play against his Parent Club (as defined in Regulation 53.1.1 below) without the prior written permission of the Parent Club (which, if given, must be indicated on the appropriate temporary loan transfer form)”).
None of which answers the question when it comes to Matty Done. After a quick look I can't find anything explicit in the FA rules in this regard (and I don't claim to have any particular knowledge in this regard). However, FIFA's rules seem clear:
3. a)The following provisions are binding at national level and must be included without modification in the association’s regulations: articles 2-8,10, 11, 18, 18bis, 19 and 19bis. .... 18bis Third-party influence on clubs 1.No club shall enter into a contract which enables any other party to that contract or any third party to acquire the ability to influence in employment and transfer-related matters its independence, its policies or the performance of its teams.
..which brings us back to Tevez, as this clause was introduced in the wake of that whole affair. In contrast to the FA's rules this clause covers both third parties and other parties to the contract, which clearly seems to cover a selling club. It seems to me that agreeing to prevent a player from playing is to "influence...the performance of its teams" and therefore banned under this provision.
So, can Done play against Rochdale? Yes. Unless he's injured...