I have a png that I need to resize to different sizes. Would it work for me to paste it in illustrator, use its auto vectorizing tool to vectorize it, and then resize it?
If you want to size the png UP you will have to recreate the entire thing if you care that much about pixellation.
If you are only sizing the png down (This assumes you have a higher-quality or large-sized png) You can turn your full-sized PNG into a smart object in photoshop, then you won't have to touch illustrator. When you make your png a smart object, you can resize it down (smaller) as much and as many times as you would like. You can even resize it up after you've resized it down, assuming you don't go over the original size.