Not really. I assume you're talking about a jpg, which is a flattened image - no layers. The only thing you can do is use the jpg for a background reference and put the layers and effects over the top of it.
You can make an psd from a image but I will stay a flatten image, as Grinderhand says.
When you publish a screenshot from a Word document, I am able insert that image in a Word document but it is impossible to reconvert it to text format. Well, jpg-psd is the same case.
That will indeed render a psd file but as grinderhand has pointed out, it will be a flat single layer image. You need to rework the image to try to separate its features into added layers to it for it to be a useful psd that you can modified (like a button) when you need it. Layered images are immensely easier to work with and get pretty spectacular results from with a little bit of creativity and practice. HTH.