For a purely military perspective, the High Seas Fleet was not disposed to prevent a British invasion of Norway. However, once the invasion was underway, German naval efforts might be more aggressive and focused to inderdict resupply and reinforcement convoys crossing the north sea. This would certainly result in more engagements between the HSF and RN than occurred in OTL. I am not so sure this would inevitably lead to a catastrophic defeat for the HSF. More likely, the Germans might send out small BC groups supported by CL and zep recon to raid the convoys. Some would be sucessful, perhaps more not, but this would not be catastrophic. An intersting possibility is that the u-boat effort might be redirected from the North Atlantic to the North Sea with significant effect. I also agree that German pressure, as well as Sweden's own inclination, might lead Sweden to join Germany. I am not sure this would necessarily doom the British invasion. Militarily, Sweden is less of a valuable ally to Germany than the Ottoman Empire. More likely it would tie down Britain until they decided on their own to withdraw.
I think the real effect would be diplomatic. A British invasion of Norway would seem little different to the world (esp the USA) from the German invasion of Belgium - thus depriving the allies of moral high ground. Plus, if it resulted in u-boat efforts directed to the north sea, Germany may have been unable to pursue the its unrestricted submarine campaign in the Atlantic to full effect. This would also have reduced a major causus belli for eventual US entry into the conflict.
Bottom line: Britain is tied down in another costly marginal front, the USA remains neutral, Russia still collapses on cue in 1917 and the Central Powers force France and Britain to the negotiating table in 1918.