G Raghavan,
Whether there was `musical influence' by Hindi or not during the pre-IR days / post-IR days cannot be commented by me (which is for musical pundits to analyze and conclude, obviously).
However, as someone who closely followed the listening trends / cultural trends of 70's & 80's (from real grass root levels -especially in small villages and small towns...big cities could have been even more polarised towards north/foreign music), I can vouch for the sea change from the immediate period pre-IR-entry and after, toward TFM...(I'm not referring to the 60's but mid / late 70's)
Pre-IR-entry : Those with gramaphone players in their home collected mostly `Hindi LP records' or `western' while TFM was reserved for commercial `sound-set' people who organized the noise for marriages and such functions (and invariably stuck to MGR-Sivaji songs). The `educated' and `elite' found pride in telling `I don't listen to TFM stuff...me only `vellai panni' (jocular reference for a famous hindi MD) etc.'.
Post-IR-entry : Though the 45 RPM continued for a while in TFM, it was fast getting replaced with the 33 1/3 RPM and IR's music was hot - not only with the `sound-set' noise makers with horn speakers, but also with those who snob around with their own musical systems...then with compact cassette becoming popular in the early 80's (with the burma bazar panasonics, ofcourse:-)), initially it was recording from radio broadcasts but later the recording centers that became very popular, all to make TFM-available-on-demand.
Certain hindi songs like qurbani were ofcourse very popular in TN despite IR's musical feasts, but it was no longer considered `elite-taste', but just another variety...