Can composing something on paper help you to be a better improviser? This question is like asking, can writing be helpful to public speaking?
Of course it can and it will. In fact writing, language, composition, and improvisation have more things in common than it might seem at first.
If we agree that improvisation is the process of composing a piece of music at the moment of performance, than it really is very similar to the art of language in that writing extensively will help a person organize his or her ideas better and be better equipped for speaking in public. I'm not suggesting that by writing alone a person will become a great public speaker. No, there are 4 total skills that are involved here: reading, listening, writing, and speaking.
But there is more to it: just like no person can become a great public speaker without much reading, listening, writing, and speaking, then the art of improvisation will encompass similar 4 activities: sight-reading and understanding the music of others, listening to and understanding the music of others, composing your own music in writing, and composing your own music at the moment of performance (improvising).
So where to start? All starting points are equally valid.
One of the easiest ones to understand is this: choose a key and a meter, and create a 4 measure melody (question) starting on one of the 3 notes of the tonic chord of that key (1st, 3rd, or 5th scale degrees) and ending on one of the 3 notes of the dominant chord (5th, 7th, or 2nd scale degrees (in minor - raised 7th scale degree).
You can use the rhythms that are suitable for this meter. Start the answer like a question but end on the tonic note. You can also add a second voice by supplying the suitable notes that work on each beat with the melody and use the notes of the tonic, dominant, or subdominant (4th, 6th, and 1st scale degree) chords.
Here's my example of this process and a video.
[HT to John]
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