An iPad 1-fitting accessory will probably not work well with it, but it depends a bit on how "form-fitting" something is.

But just for the record (not sure why you couldn't just google this, I found it in about six seconds):

iPad 1: 242.8mm x 189.7mm x 13.4mm
iPad 3: 241.2mm x 185.7mm x 9.4mm

So as you can see, quite a bit of difference in thickness there. I can't imagine a stand not working okay, but cases would be quite a different story (due to the width as well as the height).

Bottom line: if iPad 1 stuff worked for the iPad 3, every manufacturer would be overjoyed, as all that unsold iPad 1 stuff could just be re-tagged and sold at full price. There's a reason why that's not happening, but in some isolated cases (like, for example, Apple's own iPad stand, which has never changed) it might work.