Sure can - (assuming administrator or content manager rights)
1)Select the SPS area where the web  part is instantiated (displayed).
2)Click the image  Lib (in the title bar) - you should get a web page with
just the image library  (http://server/sps%20url/Forms/AllItems.aspx)
3)Click on "Modify settings and columns"
4)You should now have a page with "Customize ..library name.." at the top.
Under the General Settiings, click on "Save document library as template"
5)Fill in the File name, and Template Title .. CLICK THE CHECK BOX INCLUDE
CONTENT.
6)After the template is created  - you get a page with a link "To manage
templates in the gallery, go to the list template gallery".
7)When you click on your new template you will get a "File Download" dialog
box. Click Save - and save it to a local or network file.
8)Now you can go to you "real" portal, navigate to the "List Template
Gallery" via Site Settings and Upload the saved template.
9) Finally, you can create a new web part  via the "Manage Content" action on
the "real" portal's area using the template you uploaded.