If I play Draven Glorious Executioner, do I win a combat and draw a card if an enemy unit is pushed back by the ability of Overzealous Fan?

No. When Overzealous Fan kills itself to push your attacking unit back to Base, both players end up with zero units at the battlefield, so the combat result is "No Result" — not a win for you — and Glorious Executioner's "When you win a combat, draw 1" does not trigger.

Per Rule 466.3.d, if neither player has units present during the Determine Combat Result step, the result is No Result, and the battlefield becomes Uncontrolled (Rule 466.5.b). Since you didn't win the combat, no card is drawn.