Do the boxes on Franklin's Mansion get removed with time or missions?

Solution 1:

Speaking from experience, it seems that the boxes are moved based on mission progression, not time. After moving into the mansion I completed the Kifflom questline as Michael - which takes around a week to finish. After completing this and returning to play as Franklin the boxes still remained.

Referencing the wikia page for the mansion it is verified that the boxes are removed as the missions are completed.

When Franklin moves to this safehouse, several unopened boxes and packages appear. As the storyline progresses, these boxes disappear as Franklin settles in.