Yes they can according to AZ Phil of The Cub Reporter, quote:
16. A player on a minor league Full-Season IL must remain on the Full- Season IL for the entire minor league season and cannot be reinstated until the 5th day following the final game of the World Series.
A player on an MLB injured list can be traded, even if the player is not eligible to be reinstated and/or healthy enough to play. However, a player on a minor league injured list cannot be traded until he is both eligible to be reinstated and healthy enough to play (although the player could be a "Player to Be Named Later" in a trade).
If a player on an MLB injured list is traded, the player can be transferred directly from his former club's MLB 7-day, 10-day, 15-day, or 60-day Injured List to the corresponding Injured List of his new club. Days spent on a 7-day, 10-day, 15-day, or 60-day Injured List prior to the trade count toward the minimum number of days required before the player is eligible to be reinstated.
If a player on an MLB 60-day Injured List is claimed off waivers after the conclusion of the MLB regular season but prior to the deadline for reinstating players from the 60-day IL, the player can be transferred directly to the claiming club's MLB 60-day IL.
A player accrues one day of MLB Service Time for each day of the MLB regular season spent on an MLB Injured List.
https://www.thecubreporter.com/book/mlb-roster-rules-presented-arizona-phil-29