Theme and Variations in the Practice Room

I was sitting in a practice room a few days ago at the music school where I teach waiting to meet with my boss. I had no "sheet music" or "vocal music" 'to practice. For the past 10 years at least I have always headed to the practice room with specific, notated music to practice. Sitting in this practice room with only the piano in front of me I began to practice scales, something that a pianist wanna be like me should be practicing! After about 5 minutes of this I began to get bored and started to "improvise" on major triads. I settled on the arpeggiation of an F major chord using two octaves. To this arpeggiation I added a descant melody on a descending C major scale. (Now I am discerning the music theory elements as I am explaining my theme but in all actuality when I was creating this theme I was simply, just playing, not really focusing on whether it was in F Major or C Major.) Suddenly after about 10 minutes I had a theme. I started slowly to add onto this theme with different variations of it. For example instead of arpeggiating the chords I played blocked chords or attempted to play it in a "Pomp and Circumstance" style. I then added IV and V chords to my variation and started to create variations on that! It was really quite exciting and I had no agenda. If not for the meeting that I had to go to I could have sat in that practice room for hours and played with this one theme.
When my boss knocked on my practice room door to signify that she was ready to meet with me I was almost disappointed. I have never really sat down at the piano, which I am not the most skilled, and just played "non-notated music".
I did not notate my theme and variations and to be honest I can only remember the theme. I plan to keep working with this theme and add a few new variations. Perhaps I will try to notate it as well. On the other hand could it be better just to let this theme exist in my head and allow myself to simply "play"?