Reminder of the relevant section from the league rules:
2.3 Adding Players
Owners are free to add any unowned player with at least one MLB game of experience. During the season, adds are restriced to 6 per week. There is no limit to adds during the offseason.
Unowned players with no MLB experience that are added to a real life roster can only be added at 8PM ET two days after their MLB debut. So if they debut on Tuesday, they can be added at 8PM on Thursday. Commissioners reserve the right to manually add any such player to actual waivers, and owners can request that any such players are added to waivers.