At the end of the Saints game on 9 September 2019, would the clock have run out if the receiver had not been touched by the defender?
Assuming you are referring to the play just before the Saints' field goal attempt, the Saints actually burned their last Timeout to stop the clock.
In your scenario of the defenders not touching the receiver, the play would have been called dead, assuming the runner made no attempt to advance - ie they gave themselves up - under Rule 7.2.1 which states:
ARTICLE 1. DEAD BALL DECLARED
An official shall declare the ball dead and the down ended:
(d) when a runner declares himself down by:
- falling to the ground, or kneeling, and clearly making no immediate effort to advance.
The clock will still be running at this point, However, once the ball has been declared dead, then the Saints would have been able to use their timeout as per Rule 3.37.2:
ARTICLE 2. CHARGED TEAM TIMEOUT
A Charged Team Timeout is an interval during which the Game Clock is stopped and play is suspended at the request of one of the teams or when it is charged to one of the teams by rule. A Timeout may be granted only when the ball is dead.
So, technically the clock could have run out, if the officials had not called play dead before the game clock expired, or the Saints had no timeout to use.