No, but the rooster will "tell" you when that girl is ready to start laying. Whenever I place a mature (at least one year old) rooster in with pullets, he'll essentially ignore or 'court' the girls until he senses that they're ready to start laying. As soon as he sense it he'll mate with them, and two days later I'll get the first egg. It's never failed me. My boys even tell me when my (former) broodies will start laying, as well as when or if a hen in molt is still laying or will begin to lay.
And in regards to your hypothesis about POL, my observation is that having young cockerels in with pullets may actually delay laying because those young boys stress out the girls by trying to mate too frequently without really knowing what they're doing. A good, mature rooster by comparison knows how treat the pullet right and makes her feel safer rather than on the cusp of being raped every ten minutes. I try to NEVER put younger cockerels in with my pullets. Those boys need to mature in a separate location until they calm down a bit, but a rooster will teach a pullet how she should expect to be treated, making her a more assertive gal when one of those young'uns gets the wrong idea about her.