Personally, I have little doubt about technique being the most important factor, and by a significant margin. However, proper training will accomplish two important things:
1. Improve motor control in general and, in turn, make it easier to develop better technique.
2. Increase the power with which you can execute good technique.
So, in short, technique is not everything. Without good training, motor control will likely be less precise and more susceptible to fatigue, which translates into a heavy ball that you can't control as well as you'd like.
Power in tennis is all about the kinetic chain. If power/energy is lost during the transfer from one body segment to the next, power of the resulting shot will lost as well.
In regard to training, in my opinion, here are the most important things to focus on relating to the kinetic chain of groundstrokes:
1. Hip extension
2. Trunk stability - rotary stability in particular
3. Scapular stability