What would be the potential pitfalls in pouring a concrete patio over deck footings and then securing the posts to the slab?
I think your approach is right on target. Follow FreeMan's suggestion to embed bolts in the footings to attach your base plate for each post. It's unlikely that you'll have serious frost issues as long as you:

Make sure your support piers are below frostline - in my area it's 36&quot;.
Be certain to properly lay the patio base with a solid, self-draining material such as sand or fine granite.

If you're particularly concerned about frost heave you might want to consider going to 6&quot; depth on the patio.