Two things come to play. First, I don't think it takes much energy to evaporate the moisture in the wood. Time yes, energy no. So not much BTU's are lost due to the wood being wet. Secondly, the boiler only cycles for heat for around 20-30 minutes every 4-8 hours- depending on the outside air temp. So that means for most of the time it is just smoldering and that smoldering process dries out the wood to some extent.
I guess the bottom line is I have not noticed any difference between burning the wet wood vs. burning the seasoned wood in my boiler.
-John