To answer this correctly, you need the pre-order code. So, if you order the one that is all the previous expansion combined, then no. But, if you are ordering any of the Stormblood versions, then yes.

You just have to make sure to get the pre-order code and register it.

As for the codes coming in the box, those codes are the full Stormblood. In the past, SE has given up to a week or 2 after release to get it register or else your access to Stormblood becomes disabled. (Assuming you have the pre-order registered.) If you do not have the pre-order register, then you cannot play Stormblood till you register those codes.