Can Rules be used for gradual content delivery on a per-user basis?

I'd like each member of a site to receive access to nodes of a specific content type based on their length of membership. For example, I have 4 nodes of content type X, and I'd like members to access them in 2 week intervals, like so:

Day 1: Member A joins, sees node #1
Day 15: Member A sees node #1 & #2
Day 29: Member A sees #1 #2 & #3; Member B joins and sees node #1 ONLY
Day 43: Member A sees all 4 nodes; Member B sees node #1 & #2 only

If Rules can do this I will be elated. Icing on the cake would be sending customized notification emails for new content, but that can be fudged with a generic 'there's new content' email.

Thanks,

Arp