I'm not sure if it's been measured, but I imagine this densified wood would probably have at least twice the thermal conductivity of typical construction lumber, since naturally dense hardwoods already approach that.
So it seems like we'd basically need to replace 2x studs with 1x studs, assuming the same stud spacing, in order to match the thermal performance of a traditional wall.
I don't think this would be a dealbreaker at all though, one could always use continuous insulation instead of cavity insulation, which has a lot of benefits anyway. Maybe it can end up being a competitor to metal studs for commercial builds, at least.
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.
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