Meditation with a mantra is very well known and documented. One good example is David Frawley's Mantra Yoga and Primal Sound. Anything that is repetitive and that is attended to will create a state of trance, and if used according to the procedures given helps create conditions favorable to meditation (dharana, dhyana, samadhi). Deep meditation here is also paired with other techniques like spinal breathing pranayama, and they work together to amplify the effects.
The effectiveness of the techniques is measured by their impacts in everyday life, and not during routine practice. I use the first mantra, along with many of the other practices, and definitely notice a great overall improvement right after a single session.
