Probably not soon do to the method required and most likely after most of the other science objectives have been completed.
Spirit doesn't have drill into the soil capabilities but only a grinder tool to drill/clean the surface of rocks for an inside look of the rocks. What Spirit can do is use one of the wheels to dig a trench in the surface by locking up the other five wheels and rotating the one wheel. It will be interesting to see if they use this method and how far down in the soil this technique yields.

Beagle 2 had the capability to drill or mole into the surface but as we know probably did that on landing and won't be getting any data.

SteveS