Does Cambridge look down on private candidates?

To be clear, when I say "private candidate" I don't mean someone who went to a private college, I mean someone who taught themselves their A-levels and took them privately.

For medical reasons, my attendance at College is at 15% and they have handled it horribly to the point that they are more of a hindrance to me teaching myself at home than a help. Once I am 18 there are new medications which I can take that are far far more effective than anything they will let me take now so attending university should not be a problem.

My goal Is the Cambridge Natural Sciences course and I'm taking A-level physics, maths, further maths and computer science.

If I do take my A-levels privately and achieve the top-level results I think I can get, would a university like Cambridge be less likely to give me an offer?