For example, Mozart, Schubert, Tchaikovsky, and Chopin.
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I'd say not quite.
There is a huge difference between current rock star status and top pre 20th century classical musician. For starters, their sphere of influence was mostly limited to the higher classes, because those were the people attending concerts/operas/ballet/etc.
Mozart traveled extensively and was very well known.
Schubert was not really famous during his life. He started to "get somewhere" during his last three years, but he was nowhere near Mozart or Beethoven's popularity. His income came from teaching for some years, and by teaching I mean elementary school teacher (not the most rock star life).
Tchaikovsky was a very well respected and known composer and conductor in Russia, and was also known abroad.
Chopin was a musical celebrity in Paris and his music traveled far. He actually got kind of a rock star's funeral. See, it was delayed for a couple weeks after his death, and only ticket holders were allowed into the church (people arrived from many cities, presumably thousands had to stay outside). The entire façade of the church was draped in black velvet. If that is not a rockstar's funeral, I don't know what is.
I think a lot of what we now consider rock star life started with Paganini (rumours about making a deal with the devil to be the best violinist in the world) and Liszt (mania before the Beatles!).