If you're going to use PS Elements 8 then you may be able to run it on one of these but it may be taxing on the system.
Check out the min requirements on
Adobe for PS Elements 8.
You'll just fit it on screen as it needs 1024x576 monitor resolution, eeePC has 1024 x 600.
I don't know how you'd go with very large files or with lots of layers but I reckon you can run the basics of PS E8 in the field.
Otherwise you may want to check out some other models with a bit more grunt.