"No, Brother; there was no unfinished structure on the property when it was purchased. I clearly remember that I and two others passed by when the basement was being excavated."
Just like you I visit on an infrequent basis but I was told by family members who are active members that it was purchased some type of existing structure (not sure what stage).
I was also surprised one day when I drove by to see a lot of activity there, thinking that construction will start only to see it abandoned a few months later (its now more than 5 years later).
i think the unfinished structure is a source of income 
There is now another finished masjid less than half a mile away which was started and finished within the past 5 years or so.