We are presuming your Autoloader is in .308.
A short .308 SAAMI chamber *may* have negative headspace with long NATO cartridges. Not much, though, and the forces of chambering generally "size" the cartridge into the chamber and firing is safe, even though pulling out the live round might hesitate a bit--as in hard, then zip!!! it flies out of there.
There is a believe that such a situation can make it easier to get the legendary slam-fire, at least in floating-firing-pin designs like the M1A. The only guy to successfully replicate that used high primers and ball powder that gave resistance to the primer when they got chambered. YMMV. That does not explain the events with USGI Match ammo, though they were usually tighter match chambers....
On the other hand, a long NATO chamber is a bit sloppy with short .308 SAAMI ammo. I personally don't believe that is a safety factor, but the excessive case stretching can, IME, lead to cases breaking on extraction after only 4 reloads or so. I've since adjusted my resizing to NOT be SAMMI-Min, because my chamber is in the middle of the NATO/SAAMI overlap zone.
There are also differing opinions on chamber pressure standards, but I'm not convinced they are meaningfully different. NATO surplus, by some measurements, is lower chamber pressure than SAAMI, according to some interpretations.
As far as I'm concerned, it would be safe. It's not like the .223 Remington/M193 Ball incompatibility in SAAMI chambers--their throats are too short for safe pressures--a 5.56 NATO chamber/throat is required to shoot that surplus stuff. Never have seen data on whether M855 green tip also disagrees with SAAMI chambers.