It works like a charm.
The image that you export will be the edited image. It's always worked that way in every build of Picasa I've used, including the newest one.
Ater you crop an image and press "Apply" (which you have to do before you even see the Export choice at the bottom), the selected images will export.
Perhaps you've got more than one image selected (highlighted box around it when viewing an album) or somthing. I've never seen any problems using the export feature in any version of Picasa.
Or, perhaps you're not looking at the exported image later.
You have to open the image from the folder you exported to.
I don't have these folders (the ones I export to) as part of what Picasa shows (I limit the folders Picasa displays to one directory and it's subdirectories).
It sounds like you're probably just looking at an original image, versus the exported image if you don't see the modifications you made with Picasa.