Larry Coon helps answer this question. Thanks, Larry!
There is a 2PM Eastern deadline (11AM our time), but that’s just to freeze the order of teams picking — and the freeze is only for trades that include draft picks (i.e., trades that would affect the draft order). Once the draft commences, teams are free to make trades including picks, but it will be “Team A drafting for Team B” types of trades.
When draft trades do happen, teams usually wait until the pick is made, so they can be sure a player they want is still available. Once they agree, and the team drafts for the other team, the league is notified. At the draft, the league actually staffs their lawyers backstage for quick turnaround. The lawyers review the terms (using the RealGM trade checker), and if they approve it, it’s given to Stern to announce.
Should put you out of your misery. Only a few hours left…