Just how much is it exactly? Can it be defined? Why do we even care?
The first variable that needs to be looked at is what actually defines a stick. Now if a stick was very small, or twig size, the scope for doing any poking with it diminishes. Likewise an unwieldy stick doesn't facilitate actual poking and turns into a giant wave fest.
Clearly in order to do any poking, we're looking for maximum size that is still moderately controllable.
Also, the stick needs to be a single unit. If it has multiple ends then the act of poking closely resembles a sweep or a brush.
Therefore the ideal stick with maximum reach I estimate to be something in the order of three feet.
Now then, if the average person doing the poking is about 6ft tall, then logically the total reach capability is about 9ft from floor to top. Therefore the largest possible thing that you could poke a stick at would be that inscribed within a 9ft cube.
When you come to think of it, 729sq.ft of stuff is actually quite a fair amount of stuff to be poking a stick at. In real terms this means that you could poke a stick at small cars, elephants, bus stations, bookshelves etc. These things aren't totally unreasonable nor unfeasible to be poking a stick at so perhaps out 9ft cube is about right.
It's also incidentally about the same as enough room to swing a cat in case you were wondering.