Writing A Musical Composition's Score Without Knowing How To Read Notes?

Sure.

I would suggest, however, to pick up What to Listen for in Music by Aaron Copland if you have the time.

I believe they have keyboards that hook up to the computer, that will write the notes you play. You should look into that.

Welcome to Fluther. Lurve.

Put a note chart behind your keys and look at it as you hit the keys.

if you just want to be lazy, there are programs that you can hook your keyboard/guitar/drums up to and while you play, it plots the notes automatically. I like to combine this program and this program called beatnik that I can’t seem to find a site for at the moment. Makes life easy.

As a classically trained musician, I cannot stress enough the importance of learning to read music.

That being said, there are easier ways to write that are generally accepted by the musical community.
One in particular is the style used in ‘Sacred Harp’ singing.
Check it out, as this notation may suffice as you work to learn how to read and write in the traditional sense.