You've got it
Actually the latent heat of water does vary with temperature but your 0.6kWh holds good for the approximation we are looking at. When you burn wood it changes from a solid with associated moisture to ash (a solid but very small part of the original mass) and gases/vapours that go up the chimney at whatever temperature it leaves the stove, this mix of gases carries away heat from the wood that never gives you benefit as heat in the room. If the moisture content of the wood is high then you lose that 0.6kWh for every kg of moisture that goes up the chimney plus the additional amount of sensible heat it contains at temperatures above 100C. I guess most stoves run a flue temperature of 150-350C so this sensible heat of the excess water is also considerable.
As you say wet wood is harder to burn cleanly, mostly because it quenches the burn, this shows up as smoke and particulates, Products of Incomplete Combustion, so some of the potential energy of the wood also leaves as PICs. Worse still is the business of excess air; because wood is a complex mix of substances that burn in stages we have to add more air than is what is needed to combine with the fuel to ensure enough oxygen meets the fuel to burn it out. Good wood stoves will use 1.5-2 times the ideal (stoichiometric) amount of air but this all has to go up the chimney at the flue temperature. Thus the massflow of products up the chimney consists of excess air, excess moisture plus the products of combustion (ideally steam and carbon dioxide, even burning bone dry wood produces water)). Worse still is wet wood tends to need more excess air than dry wood, hence increased sensible heat losses from the high massflow as well as extra steam.
Bear in mind you need a stoichiometric mass of air about 6 times the mass of the burning dry wood because only 21% of the air is oxygen, the rest is nitrogen which has a free ride through the fire but still carries away heat up the flue, increase that with excess air and you see what a heat robber it can be.
I think it does but it is a tiny effect only of consequence when discussing how much moisture is regained as dry wood picks up moisture again as the humidity increases in the winter.