Leaving it outside will lead to deterioration by corrosion/oxidation.
Whilst the aicraft was in service, the kinetic heating experienced by the airframe in flight, meant that corrosion was not a serious issue.
Granted, the Concorde at Duxford has sat outside for a number of years, but I think it has /will be moved inside to the new hangar, to prevent further deterioration after exposure to the elements.
Anyone who has seen the Concorde at LHR from up close will have seen a gradual change in its appearance since its grounding.
Hoping that all are moved indoors soon so that they are preserved for the future.