Friends
The description says "Play with Friends for EXTRA LUCK!" It does not say whether that luck is the turret roll, a drop, or something else, and it gives no percentage.
No rate published
Offline income is not a number yet
Expect friend play to add luck and expect income while offline, without a published rate or currency name.
While you are away
The description says "You earn income offline!" That is income. It does not say the enemy waves keep running, and it does not name the currency.
What to do with that
Come back and spend whatever income is waiting on the treehouse upgrade. Do not plan a session around a rate this page would have to invent.
Passes such as Super XP and Super Luck also have empty catalog descriptions, so they are not a substitute for this missing rate. See the price table.