It sure does matter, overdue or not.
A score of 0-1 basically means your baby isn't engaged at all, and your cervix probably long, posterior and closed. Your chances of a successful induction like that are bugger all.

I recently had a client whose Bish. score was 3 at 41 weeks. Three days later it was 7. Then next day she went into labour spontaneously and her baby was born 3 hours after her first contraction.
It can literally change overnight, or in hours.
Please do your research into this, if you agree to be induced now (especially if this is your first baby) you'll be very lucky to have a normal birth.
GL.