I ended up doing exactly this. It worked somewhat well.The last two grills I picked up, I used simple green and a blue 3M scrubbing pad. It did make a difference.
In my case I was just trying to get the boxes as clean as possible without removing any of the mostly intact existing paint.I was happy with my results because I know that being any more aggressive was just going to start stripping that off. I suspect you were shooting for the same thing.I ended up doing exactly this. It worked somewhat well.
A weird visual trick occurred though, when I scrubbed the area (after spraying with the degreaser), it looked extremely clean.
But once I took the hose to it, and washed off the area, it re-revealed the worst of the dirty area.