It would have to negotiate an accession treaty, but it would obviously meet the criteria, so barring some politically motivated roadblocks (say, the split from England being acrimonious, or Greece and Cyprus wanting to extract a stronger EU stance on Northern Cyprus, or something like that) it should go through. However, an accession treaty needs to be approved in referendum in at least some EU member states.

See this comment subthread in MfM's diary on the Nations Of Europe, which begins with

There hasn't been a single case of breakup of an EU member state, and the treaties have no provisions about it. So we don't know what standing an independent Scotland or Euskadi would have in the EU.

and seemed to end with the position I outlined above.

"It's the statue, man, The Statue."