Short answer: No. A spot of first touching cannot be an enforcement spot for a live ball penalty.
Longer answer: Rule 6-1-7 (for free kicks) and 6-2-5 (for scrimmage kicks) elaborate that R is entitled to take the ball at the spot of first touching unless "the penalty is accepted for any foul committed during the down". In such a scenario as you describe, R has three options: a) Decline the foul and take the ball at the B20, b) enforce the foul from the end of the play (B18), c) enforce the foul from the previous spot and replay 4th down (or d) decline the foul and take the result of the play at the B18, but why?).
Earlier this year, there was a thread involving unsportsmanlike conduct fouls (live ball enforced as dead ball) in this scenario... and I don't know if we ever came to a solid conclusion then.