Auto gearboxes definitely need a change of fluid every so often, I would not like to say how often, but if the fluid is brown, it needs changing. It should be a nice red translucent colour. I'm not an expert on auto boxes but I know that the AR25/ AR35 gearbox is a development of the old GM 3-speed unit from the 70s and early 80s -and that definitely needed fluid changes. The AR35 is essentially the old 3-spd unit with an extra gear tacked on at the front (hence the two sumps) , and electronic control of the valves.
I don't know why the Omega doesn't have a filler tube. More cost cutting from GM? Or maybe they felt that with the refined electronic gear changing, the clutches would not wear so much, so the fluid would not become contaminated with burnt clutch lining, and that it would last the lifetime of the car (with lifetime being defined as the first couple of owners perhaps, rather than the extended lease of life they get when bought at knock-down prices by enthusiasts).