It's more about muscle memory, touch, and hearing than it is about trying to visualize the instrument in your head.
Source: I'm an amateur musician. Judging that even I can play the instruments I know without needing to necessarily see the instrument or the notes to play (actually or imaginatively), I'd imagine actual professionals shouldn't have a problem.
I'm a trained musician, and what I'm referring to is often called mental play[0]. Einstein referred to it as visual thinking. Many successful experts across many domains will tell you that visualization skills are a key factor in their success.
Any practice routine worth its salt includes visualization exercises. For example, players are encouraged to use mirrors while they learn in order to strengthen their visual memory, and eventually players are taught to imagine the instrument in their head, to imagine practicing. This has shown to be a viable method for making real improvements while not even holding your instrument, including boosting your muscle memory as your body learns to make stronger associations.
Source: I'm an amateur musician. Judging that even I can play the instruments I know without needing to necessarily see the instrument or the notes to play (actually or imaginatively), I'd imagine actual professionals shouldn't have a problem.