Nitrogen, being a gas, is considerably more compressible than a solid housing. Whilst the dryness may well reduce the ‘compressibility’ i.e rate of change of volume with increasing pressure, (although I am not sure what the behaviour of water vapour is so I can’t readily deduce its effect), I somehow doubt that there is a significant difference that would result in greater ‘strength’ contribution to the housing.
Certainly, using a dry gas would eliminate fogging, but I can’t really see that there would be any strengthening effect on the housing.
Given a desire for a dry gas, I would have thought the logical gas to use would be air, because all you have to do is dry it. Given that air is 70% (approx) nitrogen anyway, I can’t really understand what benefit would arise from the (presumably) extra expense of using 100% (or near that) nitrogen.
If fogging is a problem, I think a silica gel packet would be a simpler solution. If depth (i.e. the desire to take a housing deeper) is a problem, then I think building a more robust housing with fewer control penetrations would be an easier engineering undertaking than flooding a housing with nitrogen.
Finally, considering the method that a housing might be flooded with nitrogen, if you really wanted to do it: you would need two valves - one to introduce the nitrogen, and the other a bleed valve to allow the air to be forced out. You would probably need to blow rather alot of nitrogen through to achieve expulsion of the majority of the damp air, and in practice you would never achieve 100% expulsion of the air due to gas mixing going on in the housing.
As serge says, it would be a cool tool, but there doesn’t seem to be any real need…