Is it possible in the spoken variant (not in the test or somewhere in writing) to omit "the" in the sentence:

He will go to school in fall.


Anything is possible, but that's going to make your English sound a bit odd.

Students: We have free audio pronunciation exercises.

You mean that this could give some poetic touch, as if I said: " He will go to school one autumn day"?

Yes, that's true, although that's not what I meant.

You asked if it was 'possible' to omit the. I was trying to make the point that you can say in English pretty well anything you wish. There are no grammar police to interfere. Of course, there is no guarantee that people will understand what you say.