I'm wondering: Do I also have to plug my phone into the imac with a cable and enable syncing with iTunes (wired or wireless) or will the photo stream connection that I have now be enough to ensure every photo will be backed up?
The Photo Stream will send any new photo added to the Photo Stream to your Mac. It will not sync the previous contents of your camera roll. You will have to download that directly.
On your Mac, you have to make sure, that you import all photos from the Photo Stream, for example by setting your Mac to import automatically from the Photo Stream.
Naturaly, to be on the safe side, you then will have to back up your iPhoto library on your Mac as well.
I would not rely solely on the Photo Stream. System troubles or network troubles can require to reset the Photo Stream occasionally, and then the current contents of the PhotoSTream may be lost. Or you may have to restore your phone.
I strongly recommend to regularly connect your phone directly to your mac and to make a backup of the phone using iTunes. That will let you restore your phone from the backup, if you ever need to reset it as a new device. Backing up using iTunes will save the contents of your camera roll, among all other items.
And an additional backup in iCloud is very useful, if you cannot access the backups on your mac in case of an emergency. See: iCloud: Backup and restore overview