I mean it's not really the exercise itself that directly gives you a good body.
It's the hormonal effect, the calorie burn, the muscle, the good feelings...
If you can integrate push-ups/ pull-ups, air squats, lunges, bodyweight ab exercises, sprints, burpees, 5 gallon water exercises, ect... into a challenging routine, then yes I believe the "dream body" is possible.
It is possible, but you're going to have to get out of your comfort zone, and work hard. I'd recommend you do rehab routines for your back along with an exercise plan.
Im assuming you have the diet in line, which is the most important part, so I won't comment on that.