Nathan,
Yes, you can be added as a named driver on your parents' insurance policy whilst on a provisional licence. However not many insurance companies will allow this though, so you will have to contact your parents' insurer to see whether they will provide cover for you or not. There are two major problems with this approach which is worth mentioning; the first one is that if you ever have an accident while driving on your parent's policy, then your parents will lose they hard earned no claims bonus. The second problem is that the cost of adding you as a provisional named driver can be expensive. A better approach is to get learner driver insurance. This policy specifically insures drivers like yourself who currently hold just a provisional driving licence but because it is in your own name, there's no risk to your parents's NCD.