The Allies find themselves at war with Norway and Sweden, and the landing at Narvik becomes a "Gallipoli" in a colder climate.
The Turks at Gallipoli where more or less prepared, they where already at war, and could reinforce their defenses by railrod and through the Sea of Marmara. For Norway the only way to reinforce is over the Atlantic, which the British can easily prevent.
They had a link with Russia anyway, by sea to Murmansk and (in the warmer months) Archangel. Result - by the end of the war, tons of uncollected equipment were piled up there, due to inadequate rail links. It would be ditto using Narvik.
Yes, Murmansk had no railroad connection untill 1917 and the reachebility of Archangelsk was dependent on the weather. But from Luleå one could ship supplies to Oulu (railroad connection to Petersburg), direct to Petersburg, Riga or somwhere else. From there on take the railroad to the front.
The German fleet. It would tie down the Grand Fleet to sustaining the bridgehead in Norway and give the Germans an awesome opportunity to wear them down in constant guerilla operations with Uboats, destroyers, and mines. Later when German aerial torpedo bombers and mine laying became possible, things get even nastier.
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Beyond that it places the pro-British Norwegians into the German camp, gives them naval bases to use against Britain, and denies the British the massive Norwegian merchant fleet they need to supply the Entente war effort.
That is indeed bothersome, what if they also capture Stavanger and make it a naval base, like they wanted short before the end of the war? The Royal Navy would make the Hochseeflotte much more carefull.
Also there is major political fallout caused by the invasion of another neutral nation, taking away Britain's moral high ground.
Well, that was no big deal in case of Persia or Greece, so why in case of Norway?
But perhaps they could push Norway join the Entente (perhaps by promising Svalbart) or make an agreement to allow the Entente to use Narvik. Would tht be possible?
By the way, capturing Iron Ore Line would have an other positive effect:it would cut Germany off form Swedisch iron. That and establishing a reliable connection to Russia (may possibly ease the Russian shortage of ammunition '15) whould have made things hard for Germany, the main enermy. With the Turks could be dealth later without losing over 200.000 people.