Integrated ground school is a ridiculously intense six months, and instructors will tell you that you're completing many years of work in just a few months. Ground school is, and will be your whole life for that six months. It probably averages-out at six hours of study per day, every day, for six months. Any sort of job within that time is just impossible.
It's six hours a day of instruction, followed a couple of hours of compulsory computer-based-training, after which you ideally need to go over and makes notes about the things you've covered that day. If there's any spare time in the evening, ideally you need to be doing the question banks and exam preparation. I start at 08:30, finish at 16:30, with a working lunch and a short coffee break, and go to bed at 10:00PM. So that's six hours of instruction during the day, and around four hours of private study every evening. Weekends are normally spent doing exam preparation, possibly with the odd day-off once every few weeks, when not close to any exams. In five months of ground school, I can count how many study-free days I've had on one hand.
In a nutshell, it's impossible to have a job of any sort during integrated ground school. It just won't happen.
