Hi Michael,
According to the information I read about Autostitch, it does create a sperical projection.
I wouldn't call my image "complete". I've tried many sets of photos which developed into many panos, all using a tripod. I photo'ed in a circular pattern. starting from about the angle if you were to tilt your head straight down (keeping your back straight), then raised the camera and did another circular pattern, then raised it higher and higher again, ending at a tilt of angling your head straight up (keeping your back straight. The maximum lower and highest elevations were pretty much limitations of the tripod. When I did this set of photos and processed in Autostich, Autostich had trouble lining up the gray floor, white ceiling and the very close wall behind where I was standing.
Oh yeh, and I tried the photos at several zoom settings on my camera. It is such a small room, not much of the room is photographed at the same time.
I had read the information on "troubled matching" in Autostich and that was able to significantly help match up some panos, but let's face it white next to white is trouble, so is gray on gray.

Scott