I can understand your concern but I do think it's important to keep in mind that not everyone who overdoses has a significant mental health problem. Part of my job used to be assessing people who presented to A&E having overdosed. The vast majority of people I assessed were not suffering from a mental illness- they were just going through a difficult time, made an impulsive decision and in most cases regretted it almost immediately and sought their own rescue by telling someone or calling 999. So the fact that your friends DD overdosed, whilst of course it needs to be taken seriously, does not necessarily mean that she is going to have long term difficulties with her mental health and can't work, study etc.
Even if your friends DD was suffering from depression at the time of her OD, that doesn't mean she can't (or shouldn't) resume her 'normal' activities. In fact, normality, routine and a sense of purpose and structure to ones day are all very important for recovery from depression. She doesn't have to be completely symptom free to go back to uni- she can access mental health support there if she feels low in mood or stressed. Universities have a duty of care to students with mental health issues and have staff trained to deal with these types of problems. At every university in the country there will be students suffering from depression (not to mention other chronic, serious mental health conditions such as Bipolar Disorder or Schizophrenia) but with the right support and some reasonable adjustments their illness does not necessarily have to be a barrier to their learning or enjoyment of university.