Can I print on Aida Cross Stitch fabric with my inkjet printer?

I want to use my printer to print cross stitich patterns on fabric

Iron it on to Freezer Paper to stiffen it. You can also treat it with Bubble Jet Set so the inks are permanent and won't bleed if your work ever gets wet/needs washing. And even if you don't plan to wash it, stuff happens (cats + coffee cups = sadness)

Probably yes. I'd say it depends on your printer and how it's paper path is constructed. I would guess that the printers that feed from the bottom of an angled stack in the back would work better than the ones that feed from the top of a horizontal cassette underneath. It may help to use a spray starch to stiffen the fabric beforehand, or possibly glue it to a piece of stiff card stock with rubber cement. If you are wanting to just print guide lines or temporary marks you could make a mirror image print on normal paper with a laser printer, and press it against the fabric. The trick with this method is that you have to hack the printer so the paper does not go through the fuser rollers before it exits. This could be easy or difficult depending on how much you care about the printer. It will work (if it works) because the toner is held onto the paper with static electricity and will just brush off until it is heated and melted to the paper.