No, Kant thought that you could only have synthetic a priori knowledge if you already had a fair amount of experience with the world. Synthetic a priori knowledge is knowledge which rests on experience (Kant thinks all knowledge begins with experience), but it doesn't make reference to specific experiences. Likewise, analytic a priori knowledge requires knowledge of language and logic, which, of course, is not innate either. Kant doesn't think there's any such thing as innate knowledge, if this means knowledge temporally prior to any experience.

This has it about right: http://en.wikipedia.org/wiki/A_priori_and_a_posteriori#Immanuel_Kant