Lisak1 has it right.
Pools will store water unless of course you add some drain scheme at the bottom of each pool. That is very rare to add.
Although hard to see sometimes. Assuming the pools are all "full" with the pump off...when you startup the pump you will notice water flowing into the top pool but it will take a little bit of time for that pool to overflow. Same for the next, and so on. Same thing happens in streams. This happens because of surface tension and a few other things.
Same thing happens when the pump is turned off except in reverse. Turn off the pump and slowly the top overflow will reduce, then the next. The bottom pool has to have enough room to take that amount of water that still goes over each waterfall or that bottom pool will overflow.
I call this "extra" water the "charge". Meaning when you start the pump there is a certain amount of water that has to be added to the falls/stream to get it going, you charge the system.
The amount of water a system needs to charge depends on the amount of water being pumped, width of each falls, the height of the falls, surface material, shape of pools, wind, etc... First two are really only a factor in backyard systems.
Now, to the actual question...your bottom most pool can be the smallest, question is though how small and what the effect will be.
If super small and you have a very large pump that bottom pool can run dry before water is able to make its way back down. You can overcome this by turning on a water hose to add to that bottom pool while waiting for water to make its way down. If your hose can't keep up you can fill buckets ahead of time and dump those in as needed. If you run the system 24/7 it will continue to run. But if you needed to do this then the bottom pool will likely overflow when the pump is turned off.
If the pool is large enough to supply the pump while the system charges you will likely see the water level in the bottom pool has dropped. This drop can be a lot and the amount of that drop will actually be the system's charge amount. Most people don't like seeing that bottom pool being low so they add some water which, just like above, when the pump is turned off the bottom will overflow.
One more interesting thing, and what causes the biggest problem, is all evaporation will show up in that bottom pool. Takes a little thought - the upper pools are always being topped off so they're always full (while pump is on). But water still evaporates from the entire system. All that loss appears in that bottom pool. The smaller that bottom pool the more dramatic the loss will appear. Seen it many times where people come out the next day and see that bottom pool almost empty and freak out thinking they have a leak. They go online and get "great" advice on ripping their system apart to find the leak, and all kinds of goops to put everywhere making the feature look bad...all to find a leak that doesn't exist.
This is also why auto fills are added to the bottom pool.