Welcome to OCDO!!! Serbu Super Shortys are classified under the NFA as AOW (any other weapon). They are subject to a $5.00 tax stamp. To my knowledge they are not illegal to own in AK but you should check with an FFL in your area.
Although the AOW designation saved you a HUGE chunk of change on the BATFE tax stamp (as opposed to a SBS), purchasing a firearm like this STILL gets you on the same lists with BATFE that owning Class III (like machine guns, suppressors and SBS/SBRs) does.
So if your desire to own a tiny, painful and hard-to-shoot, 3-round capacity 12-ga shotgun is worth it to you to get put on a list of people who the BATFE can do "spot-checks" at any time, without announcement, for any reason (or no reason at all), then knock yourself out, bro...
Personally if I lived in AK, with the bears and wolves, I'd want a 12-ga with a LOT more capacity than the Serbu. But it's your money...