Vipassana meditation is a good practice to quieten the mind. The same can be achieved through the practice of Witnessing or inculcating the Sakshi bhav. As far as the integral Yoga goes it has no particular role as the result of quietening the mind can be achieved by taking the Witness attitude, practice of equanimity and nishkama karma. The advantage of the latter is that it is in life and in daily activities that one can practice it which is consistent with the goal of Integral Yoga. Besides it also leads to a quietening of the vital energies and their purification as well.
As to progress, all depends upon the sincerity one puts into a practice. Vipassana is not exactly a tapasya unless you mean by the tapasya relying upon personal effort. Tapasya is to concentrate one’s energies, intellectual, emotional, vital, physical in the pursuit of the Divine or the higher Consciousness or Truth. There is no such concept in Vipassana. It is a practice that appeals naturally to the sadhak who does not quite believe in the idea of God, or of the Divine as a Being. Its origin is in the post Buddhist period and from the Sankhya philosophy. Hence its great demand in modern times. However this is not the path of the Buddha which involves many other things besides. A technique as such does not help much unless it is combined with the practice of certain inner psychological qualities. That is where the failing lies. Whether meditation or vipassana, or for that matter any other method lies. People give credit to a method but what works is the sincerity of aspiration. One cannot fool the Divine by closing the eyes or sitting in a posture.
What matters in the end is the purpose, the aim in view for which the practice is done. The Integral Yoga proposes transformation of nature so that the Divine Perfection can manifest here. Its process is different. Meditation is not the only practice and in many it is not even necessary. As to progress it is impossible to access it especially in a yoga that moves at several levels simultaneously. It is only the Divine or the Master who can speak about who is progressing and who is not. I have myself treated recurrent depression of fairly severe nature in authorised teachers of Vipassana and know of people having profound spiritual experience without any outer practice. The results of yoga, especially its deep experiences take time to come and what often passes off as spiritual is often a feeling of wellness which, for all its value, is hardly spiritual in its nature.
Affectionately,
Alok Da