You are correct on this. Alls that will do is make you burn a few more cals per workout (which isnt the point of the workout), and help with your endurance a little. I still train for muscle growth when cutting.
Proper diet and training together essential to become truly "ripped." However, given an isolated training volume and corresponding metabolic expenditure, a person of adequate tone (i.e. the state of continuous muscular contraction) and mass can get cut using diet with no modification to training.
On the training end, higher rep, continuous, moderate duration resistance training (such as non-stop full-body circuit training for 45-60 minutes) has been shown to burn fat much more efficiently than simply hitting the treadmill for the same duration.
In acordance with Mavy's philosophy, why not keep training for mass if you can cutt up with your diet?