Q: Can you recover a conversation you deleted? (iMessages and SMS)

If your phone was backed up after that text was created, it should be in that backup. If you restore the backup then you should get the message back.  However bear in mind that the phone will then be back to where it was at the time that backup was made, which may mean you've then lost other info.  You can't pick and choose which bits of a backup to restore.  The only other possibility is that the text is still stored on another device - if you have a Mac or an iPad which also gets your messages.  Other than that I think you're out of luck.