Jumping in after many posts, having just read the first few...
My answer is no.
Disclaimer: I am a classical music lover who hates most of the Indian film music he hears. So why would I even bother to look at, let alone answer, this thread?
Because... when I first heard AR's music, it was like a breath of fresh air among the film music. Roja, Sanagamam, 1947... great melodies, catchy tunes, good music. In a few years, though (I had a Bolly-/Tolly- wood-loving girlfriend at the time) I felt I was just hearing more of the same, and his music no longer stood out from the rest.
He is nicknamed "the mozart of madras". I have no idea why, as, as far as I know, he was not composing great classical pieces at a very young age. It can also be said of Mozart that his music has lasted centuries, and that he has written melodies that are familiar even to those who have no idea what they are.
I have been to an ARR performance where his compositions were played by a British symphony orchestra. In my humble opinion they did not stand the test. Such arrangements of Beatles' songs do stand that test: even though composed as pop trivia, they have a depth and richness that can survive an orchestra.
Maybe it is an unfair and even irrelevant comparison, but I think that Lennon and McCartney compositions will still be around in centuries to come, I don't think that ARR's will.
Having said that, I still hear snippets from those early films on peoples' radios; they have managed to maintain their appeal so far.
It is easy to be a music snob. Not every composition has to be great; it may be enough that it is enjoyed for one day.