Do you think this is feasible?
No, I don't.
It's not just a matter of the software not supporting it (and there being no precedent for a similar site-specific addition anywhere else on the network), nor just the matter that StackExchange is a Q&A archive (not a tutorial repository for neophytes).
No, mostly the problem is correctly establishing the set of "experience buckets" to put users into and relying on them to correctly self-select. It is extremely difficult, in practice, to accurate define a set of skill level tiers that can reasonably cover the gamut of all users. Your example tiers are woefully underspecified.
Furthermore, people are mostly unskilled and unaware of it, and will tend to misdiagnose their own level of competence in a domain.
Additionally, you have the problem of appropriately cataloguing your suggested "tier-appropriate resources" -- under what criteria is something considered a "good" resource for a beginner-level user? Especially considering that vast majority of users seem to fall into the less-experienced tier, community voting on the content is not likely to be a reasonable approach. And also, who is going to curate the content for "expert" users?
Next, there's the usability problem. As ToddersLegrande points out, users are already ignoring the help center links, information that is designed to guide them right from the start. You could argue that the link is too out-of-the-way, and that by forcing a modal UX in front of them when they first sign up, you'd solve that problem. Unfortunately, users don't read dialog boxes (plus, when you are new or unregistered, the sites already display fairly large banner prompts directing you to information about what the site is about).
Finally, it's not what this site is about. We are not here to be everything to everybody, and one of the things we've decided not to be is a wiki for beginner-level bootstrapping tutorials.