In a work called "Arayar Sevai" by 'Sri Rama Bharati', the following is said about the Yoga Rahasya of Sri Nathamuni.
All the Alwars in their works have something called phalasruti, which vouchsafe certain definite benifits that accrue from singing their songs or pasurams. This might have led to Sri Nathamuni, the compiler of the Nalayaram divya prabhandham (which is also called tamil veda), to propound the essentials of well being in the work called Yoga Rahasya.
The harmonising of body, mind and spirit acheived by worship through song forms the basis of this Yoga. It restores health to the sick and happiness to the healthy.
Given this explanation, the claim of Krishnamacharya swamy receiving the Yoga rahasya in trace at Alwar tirunagari is "the original Yoga Rahasya" of Sri Nathamuni, is questionable.
So it is doubtful that, the Yoga Rahasya work which was not available to Ramanuja, Vedanta Desika, Pillai Lokacharya and other stalwarts of Sri Vaishnavism, could have been discovered by a person of current century.