I doubt that Photoshop will run without having been installed. (If Adobe allowed it to be copied like that, that would make casual piracy too easy.)
I'm also doubtful that Photoshop 7 would be compatible with Windows 7. Photoshop CS2 (also known as Photoshop 9) wasn't fully compatible with Vista. I'd be less hopeful about an older version. The Windows 7 compatibility list:
Windows 7 Compatibility Center home
only includes CS3 and CS4. (Both are supposed to be compatible.)
Are you referring to Photoshop or Photoshop Elements? If it's Elements, version 7 isn't that old, but it's not supposed to be compatible with Windows 7. Version 8 is the latest, and that is supposed to be OK.