I am thinking about buying a current manufactured Remington stainless 700 in 308. Can I shoot 7.62 NATO ball ammo in the rifle with success and what type of groups might one expect? jb

Yes, you can shoot 7.62x51mm in your .308Win.

I have a Tikka T3 Lite and it shoots NATO ammo into about 1.5-2" at 100 yards.
With cheap hunting ammo in the same rifle it will do 1.5", premium hunting ammo will do 0.75", with match ammo it will do 0.5".

The only cautions with 308 vs 7.62nato is if you have a autoloading rifle chambered in 7.62NATO, you shouldn't shoot the high energy/light magnum loads in it.

jbok,
Fumbler's info is 100% correct.