When I have these kinds of questions, I calculate the case capacity divided by the groove diameter squared and compare that result with other cartridges. By comparison the .338 Win mag is very close to the .30-06 sprg and the 7x57mm mauser, and slightly less overbore than the 6.5x55mm and the 270 win. Most people think that the .30-06 is OK with a shorter 22 inch barrel, and so the .338 should work fine with a 24 inch barrel.
One of the members her (craigwy, bartb, can't remember exactly) uses a similar formula. He uses the case capacity divided by the barrel cross sectional area in mm, and considers a value of 1.000 as an ideal.