Can you be a music composer without being able to play any instrument?
Absolutely. Music theory will help you a lot when you're composing music, but it's not necessary. Because we all inherently understand the basic elements, just by living on this planet.
You can choose to learn to compose music with or without an instrument. Beethoven, for example, preferred to compose at his piano while some others preferred to compose music in their heads and found that it was more effective. Although both methods have their different advantages, the most important thing is what suits you best.
Many composers write their music away from their instrument because they believe they will get better ideas and thus make better music. For example, Mozart and Bach used to use paper for writing and changing their music.
Some musicians believe that composing away from their instrument makes them more focused due to not distracting by the sound or customary moves they make on the instrument.
Also, composing music without having an instrument enables the composer to do it in a location of choice, which means that the composer could be walking through the woods or even could be in the traffic when ideas occur to them.
But the better way would be to try both of them to find out what your method is. However, you could also choose both of them because the important thing is what comes to your mind, not the way you're doing it!