They will have a record of your first time in training. I have flown both 135 and 121 and on my first day at both companies you assembled your training folder. We had a guy at my 135 leave during training and he had to send a PRIA request to our company. From that point on all training was logged and was under PRIA. We had a guy fired in the class before me for failing to disclose he had resigned from a major after a week.