If I follow what you are after, then no.
Savage barrels are SAAMI chambers, and spec. 5.56 NATO is a different(albeit small) chamber and pressure spec.
Given the current trend to "up the pressure" of the 223/5.56; AND the usually long throats of Savage, I doubt there would be an issue.
A few things to remember in your quest here:
1) The military uses the 5.56 in semi/auto rifles, not bolt guns.
2) Faster twists raise pressures, they also lend to bullet(non-fmj) destruction due to RPM.
3) Every gun is a little different.
4) ALL gunpowders have lot variations, so unless you have THE EXACT SAME lot as the book...
With a very few exceptions, if you want accuracy(Gamekings) they won't be AS accurate at max velocity.
You should work-up and find what max is in YOUR GUN, DO NOT expect to find the answer in a book.
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