Good question (if it can be used as a spray). The particles are quite small (basically dust) so I think it's potentially possible.
Luckily the microbes are too small to be harmed by the shards of (essentially) glass. Although if DE could kill bacteria, that would be really good in another way, because then we could use it as a natural antibiotic that never causes antibiotic-resistant superbugs! But as far as I know, DE isn't tiny enough to kill single-celled organisms. It seems to be too small to hurt mammals, too big to hurt microbes, but just right for mites and bugs.
If you have a powder made of silica, and it was derived from DE, then it sounds good! Some DE products are "baited" though, which means they are mixed with an attractant. Basically it's like bug killer, they come eat it and die. The stuff I get isn't baited. I don't want to attract bugs, just get rid of any that happen to come around! :)