Are you trying to add a picture to one of your pages or are you referring to product photos?  If you are referring to product photos, then no, you cannot upload the image without first saving it to your computer.  However, if you are referring to adding the picture to any of the pages on your site, then yes, you can copy and paste the picture into the editor window.  Keep in mind though that when you copy and paste an image from another site to your admin area, it may create a hyperlink to another page.  In addition, when you add the picture to your site using this method, it is not truly uploaded to your site, but instead it’s just copied and pasted onto your site.  Therefore, it is recommended that you still save it onto your computer first.  However, it’s up to you.