Can I transfer photos that are not in my iPhone's camera roll to my computer?
Yes, you can get the photos back on your computer that you synced to your iPhone. However, they will be a lower quality as iTunes automatically resizes them when it syncs them onto your device.

One way to copy photos off an iDevice is through a program called iExplorer (previously iPhone Explorer) that lets you access some of the filesystem on the iPhone.

Install the program from the website, then open it. You will be presented with a screen where you should find your iPhone listed. Here are the locations of the photos:

Camera Roll Photos:
iPhone -> Media -> DCIM

Previously Synced Photos:
iPhone -> Media -> PhotoData - > Sync

To get the synced photos off your iPhone drag the Sync folder into a folder on your computer and wait for them to copy. The same applies to the camera roll photos if you want to grab them at the same time.