Merely storing all the positions that are unwinnable - regardless of why they are so - would require more matter than we have in the solar system. Not to mention the efficiency of running a DB search on that...

The storage space problem is insurmountable. However searching that kind of database would be extremely efficient (if the designer isn't a moron). The search speed would have a lower bound of very close to (diameter of the sphere that can contain the database / c). Nothing more is required for search purposes than physically getting a signal to the relevant bit, and back, with only minor deviations from a straight line each way. And that is without even the most obvious optimisations.

If your chess opponent is willing to fly with you in a relativistic rocket and you only care about time elapsed from your own reference frame rather than the reference frame of the computer (or most anything else of note) you can even get down below that diameter / light speed limit, depending on your available fuel and the degree of accelleration you can survive.