From my understanding you're on the right track with respect to it being the inspiration, so to speak, for the .308 being developed by/for the US military. I don't believe it's the true "parent case" of the .308 however. The .308 is the parent case of the 243 Winchester, 7mm-08, 260 Remington, 358 Winchester, 338 Federal.
The 300 savage was developed, and most likely developed around the marketing that it would push a 150 grain bullet to 2700 FPS, which is what the 30-06 was advertised as doing back in the early days. It left the 30-30 in the rear view on ballistics, and for a woods rifle it still is as good as the day it was first chambered.
I have gotten 2700 FPS from a 20 inch barrel M99E with 150 gr bullets (150 CoreLokt, Speer Mag Tip, Hornady 150 Spire point, original Barnes X) with IMR3031, IMR4320 (discontinued) and Varget.
Felt really guilty doing 2700 fps... 2550-2600 fps with a 20" barrel and that rifle felt a lot better on my conscience. No issues, but I got over the quest for every last fps right then and there during load development. I don't know there was ever published data for Varget, however extrapolating from loads with those powders in my other rifles and crosschecking load data with similar cases, I started low and worked up.