Being part of the profession and being from a less well off background I would say no. As I am sure would most of my colleagues.
Yet I know that many of my patients and friends from where I grew up would say yes. There are many reasons for this.
Doctors are seen as the high fliers of society (one of them anyway) and many people see social mobility as somehow taboo or very difficult. I can certainly vouch for the fact that social mobility is difficult. When I went to university I felt many fellow students did not want to know me as I did not have family connections, or able to go on holidays, go out all the time to the best clubs or do a wonder of things that required wealth of some description. I clearly remember saying I had no money to a friend (meaning I had about £2 in the bank until my next loan cheque went in and they were trying to convince me to go out as I would only be spending £10 or so. In addition to this I found it very difficult to relate to many people from home who did not go to uni, someone who has a job as a check out assistant can feel that they are very different to someone who is studying to be a doctor (even if that medical student does that job every summer).
Second, the actuall going to university is seen as prohibitive to many from less well off backgrounds. Telling people they have to get into debt (however that debt is paid back) is going to put a large number of people off when the only experience they have with debt is that of their parents who may not have had the best time paying it back.
Finally, for many families losing a member who could contribute to the family income to uni where they may end up needing to empty the family coffers more is out of the question.
No matter how much we encourage poeple to apply to university, this isn't going to change. Unless we pay people to equivelant of a living wage to study (for everyone and not dissadvantage those on middle incomes) and do not charge tuition fees these factors are always going to play a part.