Could a Soviet-conquered Finnish government potentially hole itself up on the Aland Islands? (the question is who would back such a regime in the middle of WW2 in such a way that it could survive the war)
While intriguing, the option is not very likely. The Ålands were one of the main areas the USSR wanted to conquer in Finland, and indeed a a focal point of many Soviet-Finnish talks, formal and informal, during the late thirties. They control the approaches to both the Gulf of Finland and the Gulf of Bothnia and can act as a forward base to menace Stockholm from. I have never heard any Finnish plans to use the islands as a base if the mainland was lost, only as a conduit for withdrawal to Sweden and points south.
Now, lets say if Finland accepts Allied help in 1940 and Sweden and Norway too are brought to the Allied side, I could see the Ålands acting as the interim "Free Finnish" capital at the time of a general withdrawal from Finland in, say, Summer 1940. But I very much believe Stalin would not have left Mariehamn alone had rest of Finland fallen and the USSR got involved in a general war against the Allies. The strategic importance of the islands is way too significant for that.
Berra said:
What was the guy who signated to take over Finland had Soviet taken over.
http://en.wikipedia.org/wiki/Otto_Wille_Kuusinen
Possibly, however, the original candidate for Prime Minister was this guy:
http://en.wikipedia.org/wiki/Arvo_Tuominen
He claimed in his memoirs that Moscow tried several times in November 1939 make him to return from Stockholm to the USSR to run the Terijoki government but, having already fallen out with Soviet leadership, he consistently refused the offer. That is his story, anyway.