No, I don't think so.
With the best reloads possible, that rifle might keep 5 shots fired in 5 minutes inside 25 inches at 1000 yards with the action epoxy bedded and barrel free floated. That's due to the barrel; not the action, stock nor sights.
The .308 Win. chambering's best for long range accuracy with that rifle. Much easier to reload accurately for as well as having good commercial match ammo available.
Few, if any, factory rifles picked at random will shoot that well. Savage has some that'll come close and 1 or 2 that might do it. But only with the best reloads possible.
There's not any significant difference across several 24, 26, 28 and 30 caliber cartridges used in long range competition. They all will shoot under 6 to 7 inches at 1000 yards in good conditions with proper reloads shot from well built rifles. And occasionally, they put a really tiny one down range that gets everyone's attention. Doesn't matter that the tiniest groups come from all the variables pretty much cancelling each other out. And the biggest ones happen when all those variables add up in one direction. Both happen at about the same frequency.