As far as I am concerned, classical music in conservatoire includes music theory and instrument trainings. To play in an orchestra, especially semi famous one, most likely you would need to follow an university/similar degree.
Any exam is done without a music sheet, music theory always include composition.
Chord progressions comes surely later in music theory but harmony is key from classic repertoire,and counterpoint from baroque era repertoire.
Oh, absolutely. I'm not saying that a professional musician at a major symphony doesn't know about theory -- this guy I took out was clearly very accomplished in his field and went to conservatory for it. Even the classical education I had up through high school included harmony and chords. But there is a difference between knowing the theory from a technical perspective to be tested on, and completely embodying it and using it to make music. Here's a recent video of my friend's group playing [1] -- everyone involved has a world-class level of understanding of theory, but uses it to improvise, not just to read sheets.
And let's not forget that a lot of 'classical' musicians back in the day were expected to be able to improvise as well. There's just a different priority for a 'classical' performer these days and a 'jazz' performer.
Any exam is done without a music sheet, music theory always include composition. Chord progressions comes surely later in music theory but harmony is key from classic repertoire,and counterpoint from baroque era repertoire.