I think you can definitely create a different persona based on time. Critical goals of a new user could be different from a returning users so creating a different persona makes sense and could help you better identify the tasks that the user is trying to accomplish. For example, consider two people using a smartphone:
- Kat (new user) just got a new Android phone for Christmas; she is really excited to start using her phone and make it personal. Kat's previous phone was a simple Nokia phone that she mostly used for making phone calls. Kat is excited about Android because she hears that it can also have a Facebook.
Goals: Change home screen background and ring tone, set up Facebook.
- Jack (experienced user) had an Android phone for a few years now. Jack is very active on social web and follows many blogs on regular basis. When eating breakfast Jack enjoys reading new posts about astronomy; he likes to tell his friends at work what he read and share interesting articles with them. Jack travels a lot; when flying Jack likes to read.
Goals: Quick access not latest posts about astronomy, read astronomy posts when on the plane even when connection is turned off, email links to the posts to his friends.