Does my multiplayer Galaxy at War progress count towards all my single player saves?

If I've got substantial Galaxy at War progress via the multiplayer mode, does that carry over to each different playthrough or save I might make?

For instance, right now I'm doing a Paragon run. If I opted to restart the game with an evil Shepard, would I have to play more multiplayer on that profile/save in order to gain credit for it, or does my progress apply across all my playthroughs?

The Galaxy At War progress is a simple multiplier that applies to all your saves, new and old. I've confirmed that my several characters all get the same Readiness bonus. after playing multiplayer.

War assets provided from promoting a Multiplayer character are different; like all war assets, they're tried to your Single player save, so if you promote a character, they won't be in your new save.

Unfortunately the Mass Effect Wiki doesn't confirm this but my own playthroughs have.

The galactic readiness does not vary between single player saves, but it does decay at a rate of 1-5% a day until it reaches 50%.