At 19 weeks, the roosters are still adolescents with hormones running wild. They are bigger than the pullets and can force them if the pullet resists. Pullets that age are usually not sexually mature enough to cooperate, but I have had some that willingly accept the roosters attention at a surprisingly young age, long before they are ready to lay.
I saw a 14 week old pullet squat for a 14 week old rooster yesterday. That is unusual for the pullet, not the rooster, but I find that chickens are not real consistent. Each has their own personality. Usually, when a pullet willingly accepts a roosters advances, it means she is ready to lay. Usually, not always. But at 19 weeks, you should not be that far away.
Back to the question. What does the rooster have to do with the egg production? He can still have his fun but that's all it is. Unless I've really missed something.
The rooster trying to mount the pullet has very little if anything to do with whether the pullet is about to lay. Her accepting his advances is a sign she might be ready to lay. You are right in that whether or not a rooster is around has nothing to do with when a pullet starts laying. It is her accepting that is a decent indication she is ready.