Yes — if only because you can play the other instruments more beautifully. (A good guitar is hard to play, too, but it’s also harder to improvise, because you have to be able to follow through on whatever line you’re trying to improvise on — so the other instruments aren’t so easy to hear.)
In fact, one of the reasons for this is that one of the fundamental characteristics of music is pitch — it changes the pitch of each instrument, which allows the two to “talk” to each other.
And because we usually learn music over a prolonged period of time, we start developing the ability to pick out sounds that correspond to the notes of the music we’re learning, or to the way these melodies are meant to be played. In fact, you don’t develop good musical ability while listening to the radio — you develop it as you listen.
If you want to play a particular part, or if you want to play it as a specific form, you have a particular set of expectations — and a lot of our ability comes from understanding how the music we’ve come to love works with the conventions of the genre (in other words, we develop the ability to understand how the music in our heads might work, using our brains to develop the ability to play that music well over time).
Because music isn’t always a given.
• Your teacher has told you “this is a bar” so many times that it’s hard to see what’s exciting about the music.
• You like music in general but don’t particularly like bar lines.
In practice, you will discover that if you want to improvise, you have to figure out the rules of your given genre, and then work to develop a specific set of conventions for that genre. And even if a given genre works well with music you enjoy, a rule in that genre may not work in another genre — if it’s too different, you won’t be able to do it well; if it’s too standard, you’ll sound very flat.
Now, we can still learn music simply by listening — and it may just be faster and more efficient, and it may also help you learn more quickly and fluently if you have a specific set of rules of your genre, but in the process we get to discover more about how the music is actually played, and how this helps us understand the rules well enough to play (or improvise) well with our new rules.