As a player myself, and having seen much higher level player than me, reading the spin from the ball rotation (and in fact trajectory) of the ball is a common (if advanced) skill. Sometimes the movement of the bat can be deceptive (since with the same movement, where it contact on the bat, the finger pressure can affect the spin).

For example, backspin/underspin balls will move slower after the first bounce and feel 'damper' while topspin will jump. So it's def. possible (and in fact reliable) to read the spin from the spin and trajectory of the ball.

Visually reading spin is unreliable at all levels; the ITTF passed the two-color rubber rule requiring one black and one red side to neutralize players taking advantage of their opponents being unable to read the spin from watching the ball rotation via twiddling rackets with the same color rubber on both sides, but different characteristics.