I think as long as you bid on a player before getting to your max squad size, you will can still land the player (it says you can negotiate, but it still logs the number you tried to offer if I remember right).
So in theory you could land a play up to 7 days after hitting you max squad size
1)Bid on player (closes in 5 days)
2) hit max squad size (closes in 4 days)
3) (closes in 3 days)
4) (closes in 2 days)
5) (closes in 1 days)
6) (closes today)
7) Negotiation day 1

Negotiation day 2
9) Player will arrive if successful - 8 days after bidding, 7 days after max squad size.
This is not a good strategy, but it is possible (I lost a $20M+ youth by being over squad max)