Will they? Miners still have to process and transmit the full data if they are to really validate the transactions that they mine. The space and bandwidth savings will be realized only by simple clients and nodes who do not need to validate the signatures. So why would the miners give discounts for transactions in the SW format?
But they should not worry, since the space savings will only occur if the clients start issuing transactions in the new SW format. Which will not happen right away, if SW is deployed by soft fork. And even after the clients have upgraded, the use of SW will be optional. Will there be incentives for the clients to use it?
No, regular transactions get a 75% bump in space.
IIUC, segregated witnesses requires a different signature format (achieved through a scripting hack to avoid hard forks) whereby the signatures are moved out of the tx body and are not included in the tx hash. That allows the signatures to be sent and stored separately. Regular transactions will still have to be stored in full in the blocks. Wallets willnot be issuing SW trasactions until they upgrade, and (since it will be a soft fork) they will not be required to.