In theory witter could persist tweets to disc and reload them at startup, however that's an overhead in itself, and leads to questions like how many do you store, how and when do you clean up etc etc.
it's not something I'd consider a speed improvement as such, though it would in theory be faster to seeing a tweet (depending on the cost of loading the data back into memory), but only to seeing a tweet you've already seen.

to be honest it is not high on my list of things to add.