Bonus question: What sort of plans did Sweden have in place for this eventuality? Although they were a neutral power, I can't help but assume that push-come-to-shove, they would have been inclined to throw their lot in with the West, so was there any secret policy discussions on that matter?
[1970s - Scandanavia - Battle]
In a nutshell, holding on to Norway.
The North Sea, and the entrances to the Atlantic, over which US personnel and equipment would have to travel, is basically a NATO lake, surrounded by Norway, Denmark, Germany, UK, Iceland and Greenland. In order to properly support anything going through the G-I-UK gap, seizing North Norway both cuts some of the distance to travel, and also reduces the chances of interference from aircraft based in Norway (and shorter ranged naval vessels). Seizing South Norway opens up the Baltic Sea, not that there was quite all that much bottled up in there. But then, it would also close off the Baltic to NATO.
I suspect you are correct with Sweden, but I've not seen anything particularly authoritative.