You cannot edit pixel images in Illustrator.
That's rather overstated. You can apply Photoshop Effects in Illustrator, rasterize ojects, and create raster-based effects; all of which is, in fact, editing pixel images in Illustrator.
Are there any tricks with this software to help disguise grainy photos?
Generally speaking, reducing grain is a matter of blurring (averaging color values). Smart Blur is one of the Photoshop filters installed with Illustrator. Disguising grain would be a matter of special effects, and there are dozens of Photoshop filters included with Illustrator for that. You've already tried one: Crosshatch. But beyond just telling you to try them, no one can advise you without seeing the image.
They seem to have gotten worse once I imported them into AI and even worse after that once I reduce their size.
Simply importing a raster image into Illustrator does not degrade it. The on-screen display of the image is poorer than in a proper image editing program when not zoomed/scaled to 1:1. But that doesn't reflect the actual quality of the image. And that's partly why the various raster filter dialogs provide their own previews.
Or is it only Photoshop that does the job...
If you're going to do much at all with raster images, you need at least a basic raster imaging program. Illustrator can't even properly crop a raster image. But Photoshop is certainly not the only program that "does the job." Corel PhotoPaint is a quite capable alternative to Photoshop, and Corel Graphics Studio (Draw, PhotoPaint, more) can be had as a competitive side-grade for much less than Adobe's bundles. Xara Designer Pro is a very versatile illustration program that can do much more image editing than Illustrator, and can be had for significantly less than the price of Illustrator alone. And as someone has already pointed out, there are even open-source image editors that you can download for free.
JET
