How important is getting to shadow a doctor before applying to medical school?

Not at all, not even slightly. There is a common myth that unless you have shadowed a doctor or had experience in a medical setting you will not even be considered for interview. What medical schools look for is academic ability, commitment to public service and good communication skills. As long as you can demonstrate all three of these very well in your personal statement you should be fine. For example working at a local scout group or volunteering in the community (i.e. in an old people's home) would be an amazing way to demonstrate your skills that exam results simply could not do. Some students are lucky enough to have experience in a hospital setting however this is not possible for many students who simply don't have the connections to acquire such sought after places.