No. The storage isn't on the SIM, it's on the motherboard.
There's a pproject in the works to make a modular phone. Then you could remove the storage module and replace it with a larger one. but there's no phone you can add storage to yet. (You can add an SD card to most phones, but that's for data storage - even though a few apps will run from it, don't count on it - Android uses Linux, not SUN OS.)