We are talking about doing this transmission swap to a 03

, I would think that this kind of swap has not been done yet unless there is by fluke only one person who has done this, nobody here can give you an idea of the time it takes and the problems they ran into doing it.
The car would still have powertrain warranty remaining ?, so right there you would void whats left if you did the swap.
The way I see this mod being done if you would still attempt this is to buy a rebuildable from the
wreckers and swap the parts required for the change, cost and time invested unkown. If this is your only car it would be off the road for some time.
Before going any further I would be at the dealer checking to see what else is different from an auto to stick (beside the obvious)To see if the part numbers are the same for the ECM, caytalitic converter,motor mounts and other parts mentioned in previous posts.
My answer is find another car in your area thats stick make a trade, take a loss maybe you'll get what you want and won't end up with two cars not running in your driveway

, it's not worth the headache and the cash out lay to swap your current vehicle over.
Yes you can turbo an automatic as turbo's run off exhaust gases I'm not sure if they are available for Corolla's.
What reason do you have for wanting to change anyway