But what they might not realize is that the joy of improvisation is available to all of us regardless of how far an organist is progressed in music theory if only he/she is curious enough to try.
Here is an example of how you can create an improvisation based on major chords only. It sounds colorful because I avoid intervalic relationship between the chords that are characteristic for tonic-dominant and tonic-subdominant (perfect fourths and fifths). Instead I use major and minor thirds, seconds and a tritone.
All you have to do is to choose a meter (in this case 4/4), a prevailing unit value (in this case an eighth note), a few rhythmical figures (here I use the rhythms suitable for march - dotted, long-short-short etc.), a texture (in this case a single layer chordal texture without the pedals), a form (in this case ABABA), a registration (in this case 16' and 8' reeds on two manuals) and off you go.
Yes, you will do better if you learn the foundations that teaches about various scales, modes, intervals, chords, polyphonic devices etc. in the long run but no, you don't have to have a PhD in music theory to start.
Try it tonight and share your experience here.