Often, but not always (one common issue is the size of C can be very large). Even if you measure all the symptoms, and are interested in the effect of the medicine conditional on these symptoms (what they call “effect modification” in epidemiology) there is the question of confounders you did not measure that would prevent p(Y | A, C) from being equal to the effect you want, which is p(Y | do(A), C).
Often, but not always (one common issue is the size of C can be very large). Even if you measure all the symptoms, and are interested in the effect of the medicine conditional on these symptoms (what they call “effect modification” in epidemiology) there is the question of confounders you did not measure that would prevent p(Y | A, C) from being equal to the effect you want, which is p(Y | do(A), C).
I suppose that’s what randomized trials are for.
Or you can read my dissertation if you want to answer these types of questions but can’t randomize :).