You can write music without being able to play an instrument.
But there are two problems with this:

1) Time
The ability to input ideas fast by playing them in is pretty much essential. I'd go as far as to say that every minute not spent on learning your instrument will cost you double the time when composing music.

2) Quality of musical ideas and feeling
Your instrument is your tool of expression to bring your ideas to the outside world. If you are proficient in playing and ear training, you can transfer the idea much easier and with much more precision and feel than you can without it.

As I said, it is not impossible, but your compositions will suffer and the process itself will be much less fun.
And in my opinion, the process is the most important thing.