Air has very low thermal conductivity, so for a lot of materials, thermal conductivity is primarily a function of how much air they contain and how it's structured (ideally in tiny pockets to minimize heat transfer through convection). Like spray foams, fiberglass insulation, etc are basically designed to hold air while minimizing convection.

I believe that's somewhat true of woods as well - different woods seem to range from 0.12-0.25 W/(mK) or so, which is somewhat less conductive than the underlying compounds like cellulose (0.4), thanks to the trapped air in wood.

It seems like densifying wood would mitigate the insulation contribution of trapped air, causing thermal conductivity to approache that of the underlying compounds like cellulose, though I'm not sure exactly what those compounds are with their process and how close they get to that air-free extreme.

if you dont make any other changes, it will have some detectable impact, but conductivity is linear with all of conductivity, depth, and area; and the other dimensions can also be changed like the screw diameter/pitch or the dimensions of the stud.

its very unlikely that this change will be an important consideration for house building or shopping though. theres simpler spots to reduce heat loss, like double paning your windows