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Yes you would!
But more accurately than "region of Norway" would be to say it's in the Norwegian Sea/North Atlantic, and the path of totality touches land only in the Faroe Islands and Svalbard.
Having spent two weeks in the region in March this year I would guesstimate the chance of seeing totality from land to be 5-10%. And the chances of seeing a good aurora display, a couple of years past solar max, simultaneously with totality would be far less. Keep in mind that from a place lake Faroe the aurora would be visible towards the north (unless it's a massive display) and the sun (during totality) would sit low on the south-eastern horizon.
Even so, I'm tentatively planning a visit...
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