Sorry but I do not see a lot of point in it, not enough to be worth all the dust that the cat will inhale.
Fleas do not breed on the cat, they breed elsewhere (so the majority of your efforts need to be directed to eradicating them from your household as much as possible; if the cat goes outdoors she can still pick more up but keeping the house basically flea-free will help a lot and is really all you can do.)
And DE has no repellent properties so it won't protect her in any way from fleas hopping onto her from the environment and biting her.
Take care of the mats, though. Fleas or no fleas. They can snowball into Trouble pretty fast, and are vastly easier to remove when they are still quite small and mild.
Good luck, have fun,
Pat