Does the Homeland produce resources while offline?

The Homeland is the customizable personal base you unlock, and the Aniimo you station there are what make it produce. Assign creatures to it, close the game, and the resources pile up without you. It also ticks in the background while you are out in the world doing something else, so it is never competing with whatever you actually want to be playing.

The cost is that the clock is a real one. Generation is measured in real-world time, not in time played, so you cannot sit at your base and farm it faster, and a long session does not buy you a bigger haul. Hours where nothing is assigned are simply hours that produced nothing, and you do not get them back.

That turns the Homeland into a habit rather than an activity. Assign your Aniimo before you stop playing, collect when you return, reassign, leave. The full early-game routine, including where this sits against your other priorities, is covered in the beginner guide linked from this page.