I'm as sure as I can be, without having stayed there, that they'll hold your luggage for you.
Since you'll be across the street from the main entrance, that means that you will have to go through bag check with your bags, having them all opened and looked through, to get TO the lockers.
The BIG lockers, the one that might actually hold your stuff, as far as I know (I actually know that the Jumbo ones are huge, but I do not know if there are or are not Jumbo sized lockers in the esplanade), are actually on the DownTown Disney side back in the "picnic" area. To get there from Desert Inn you'll go through Harbor-side bag check, walk through the esplanade, go OUT bag check on DTD side, then to those lockers. When you have your room...reverse it. With all bags being looked through, all zippers open, etc etc.
Call Desert Inn, get confirmation that they'll hold your bags.