In short... Yup!
If you keep in mind that A-Square just took it upon themselves to put their name on a catridge that's been around in one form or another for almost as long as the 30-06 itself, then you'll see that you shouldn't be too concerned with ammo availability.
The A-square should be nothing more than a aught six that's been necked up to .338 caliber. The actual dimentions might differ a bit here or there - a chamber casting might be in order, just to be safe. If it is a 06 that's been necked up, then you could use 30-06 brass all day with this one.
Elmer Keith was instrumental in fielding the 333 OKH, and used it to great effect hunting big game back up there in his mountains. I've a picture of one of his rifles that was chambered in 333 OKH - a converted Model 1917 Enfield. Nice looking rifle. Anyway, his cartridge is a kissing cousin to the 338-06 AS. The real difference being was that back then, .33 caliber bullets were common. They aren't now, but we've got the 338. I think the actual size difference is something like .333 as opposed to .338.
The 338-06 is a good idea. Loaded right, it is a powerful customer, and there is a lot of different bullet weights and types available in .338 caliber. It won't match the performance of a 338 WinMag, but it will come close, and it'll do this without the belt and all the added powder. I wouldn't hesitate taking one ofter Moose or Elk.
Unkel Gilbey