Yes. Every render the assistant produces in chat carries Upscale and Edit links under it. Selecting one opens that page with the picture already loaded, so there is nothing to download and re-upload.
What happens when you select one
The link passes the picture's address to the page, and the page pulls it into the canvas exactly as though you had chosen the file yourself. From that point it behaves like any upload: the same size and format checks apply, and on the Edit page you still have to mask an area before anything will generate.
When it does not load
If the picture cannot be fetched you get "Could not load that image. Upload it manually to continue." and an empty page. Your own browser does the fetching, so this is what you see when the picture is no longer where the link points, or when it sits somewhere your browser is not permitted to read. There is nothing useful to retry: save the image out of the chat and upload it by hand.
Opening it costs nothing
Loading a picture into Edit or Upscale is free. The credit is taken when you press Generate, and that charge is separate from the free daily renders you get inside chat. See Renders in chat are free each day.
The Jobs and Assets pages do not offer this
There are no Upscale or Edit links on either of them. Those pages give you a download and nothing more. To carry a finished job into another tool, either use the links in the chat that produced it, or download the file and upload it yourself.