I've been very mentally ill twice in my teens.
The first time at 14: generalized anxiety disorder after traumatic event. Several panic attacks a day, heavily medicalised, etc. My parents were fantastic: sought every kind of help, really facilitated things for me regarding school by going, explaining the situation, etc. I had a free pass to get out of lessons and talk to the school psychologist, could arrive later and leave earlier at school. Missed lots of lessons due to sheer panic. Was able to leave that school to my country's equivalent of sixth form with very high grades and a very generous scholarship to an excellent school.
Second time at 17: severe, severe depression, to the point my doctors warned my parents to hide sharp objects from me. Again: best help money could buy. New psychiatrist, at my request, which was private and wouldn't be covered by medical insurance. New psychologist, same. Talked to school, sometimes I would go for one lesson a day. That was celebrated, because I had managed to get out of the house. I was at a school system that required a minimum grade of 70% in all subjects to graduate, and I didn't get to pick my subjects: That year, I had 20 different teachers. I nearly failed Chemistry, and had to go to "summer school" to achieve that elusive 70%. I did, and I never saw my parents as happy as they were when I graduated high school.
I was emotionally exhausted after all that. So I asked my parents for a year off before university. They agreed, but said if I needed more than a year, I would need to find a part time job, seeing as many friends of my parents' had freeloaders for children and they were wary I might follow the same path. I didn't, of course. Eventually got accepted into the very best university in my country, and am now about to graduate.
So yes, if I were in my parents' situation one day, and I could really help my children, of course I would do so, because I can acknowledge how much my parents' help helped me before. Frankly, I'm not sure I would be here today if they hadn't done so much for me.