It was a reality for the years 1814-1905! However, Norwegians weren't all too happy about the Swedish-dominated union and in 1905 they managed to break off and gain independence for the first time since the forming of the Kalmar Union in 1397.
No, the rule is that you use "an" prior to a vowel sound. But occasionally, vowels start with consonant sounds and consonants start with vowel sounds. That's why you get things like "an hour" - or "a union".