The contract year, IIRC, ends the last day of February every year and the player draft is a part of the CBA. Even if the players aren't technically NFLPA members until after the draft, there would likely be lawsuits as to whether a post-CBA draft would be legally binding without the sanction of the CBA which serves to work around the anti-trust laws.
For example, Player A loves the Cowboys but hates the Giants. Subsequently, Player A gets drafted by the Giants this April. The Cowboys decide to poach Player A with a contract which the player signs because he's "always wanted to be a Cowboy".
With a CBA, the player is bound to play in the NFL only with the team that selected him in the draft with the blessing of the NFLPA. Without a CBA, Player A (or the Cowboys) might argue that he's actually a free agent since there is no contract that binds him to the results of the draft.
If this went before a judge or the NLRB, they would likely rule that the player is a free agent and can play for whomever he wants since there is no CBA establishing the legality of the player draft whose primary purpose is to eliminate the leverage that the player has in shopping his services to the highest bidder.
My feeling is that the NFL will try to move up the draft to February, while there is still a CBA, so that the draft is legal unless the CBA specifically states that the draft must be held after March 1st each year.
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