The player must have been on your roster before the transfer deadline. The number of games played is irrelevant.
This is completely false. For numerous reasons. Please kozlodoev don't confuse newbies.
Only initial deadline i.e. when the player was put on transfer list matters. If it was to late you will see a warning on his profile that he won't be able to play in play off (or play down too!) of this season for your team. It doesn't matter where you will obtain him as long as it is at least 15 minutes before the first play off game (I can't imagine that long bidding worse that he wouldn't be sold by that time).
Otherwise it would be a nonsense - biddingwars can change deadline of any transfer by a lot minutes thus potentially breaking that eligibility deadline if it worked as kozlodoev wrongly answered. And of course newly generated teams which happens to make play of or play downs would have none players to play woith in them if genreated after the eligibility deadline. So it is obvious kozlodoev doesn't know what he is talking about.