They do, but within limits. You can't make any random movement and hit the ball somewhere useful.

The existence of feints is why I knew people were using the body motions as a strong signal in the first place.

This is most obvious in soccer and basketball where you’ll see two similarly skilled players almost get stuck in place trying to predict the other’s next move.

Well, Ronaldo could hit a soccer ball after lights are cut.

https://www.youtube.com/watch?v=aoScYO2osb0

close but not really. the lights were on at the kick. he couldn't make contact with an invisible ball

There was an experiment done on training for basketball players where a group was told to train for a couple of weeks 3 point shoots.

One group trained normally, as in, they would position themselves and throw the ball.

Another group trained the same way, except they had no ball. So they had to position themselves and throw an imaginary ball.

A final group was obviously told not to train at all.

The results of this study showed similar progression between the ball group and no ball group and no progression for the no training group. And the study continued on showing that the exercise of repeating the pattern even without the ball strengthened the neural pathways that are usually activated when doing the action. From brain to arm and that a big part of "learning" is not actually adjusting but reinforcing.

So I imagine the players in tennis would definitely be able to hit the ball if they trained without it. At least to a certain point (adjusting is important as well obviously).