The SNP's new plan is based on its belief that "negotiations will be required in advance of independence with the European Union to agree terms of an independent Scotland's continuing membership."
However this would seem to contravene EU law. The EU has a clear process for EU accessions set out in Article 49 of the Treaties as follows:
"Any European State which respects the values referred to in Article 2 and is committed to promoting them may apply to become a member of the Union. The European Parliament and national Parliaments shall be notified of this application. The applicant State shall address its application to the Council, which shall act unanimously after consulting the Commission and after receiving the consent of the European Parliament, which shall act by a majority of its component members. The conditions of eligibility agreed upon by the European Council shall be taken into account."
So to apply to be an EU state you must firstly be a state, (i.e. not a pre-independent state) and that, once an application is received by the European Council, all EU states would have to agree to membership. There seems to be little room for ambiguity and is helpfully explained on the EU's own website here.
And if this was not enough, the EU, under Article 4, has a responsibility to "respect the equality of Member States before the Treaties as well as their national identities...including ensuring the territorial integrity of the State." It is difficult to see how negotiating with Scotland pre-independence would conform with that duty. Something Spain would probably point out even if the UK did not.
Even if informal negotiations were opened, could the EU conclude any of the negotiating chapters with a non candidate non state (probably not), could Scotland prove it has the capability to live up to its EU responsibilities prior to independence (again probably not) and how long would the negotiations take - probably years.
But this comes to the biggest problem for Scotland. They would need to get all 27 states' approval. Unfortunately for Scotland some states have a strong principled opposition to succession. Spain, Romania, Cyprus and Greece (and the EU) for instance still do not recognise Kosovan independence. Scotland's potential case is obviously very different, being based on consent, but the principled opposition, from other member states, could be the same. There are also unexpected bilateral issues that any EU state (apart from the UK) may wish to bring up, fish is perhaps the obvious one (and troubled Norway's accession negotiations) but for the sake of argument the sovereignty of Rockall could be another. It is difficult to tell - Croatia's EU bid was held up for years by a dispute over maritime access with Slovenia.
And that is even before Scotland raises the question of opt-outs to the euro, Schengen, fish and issues surrounding the UK rebate, budget and the number of MEPs it might want...
Of the 27 states that need to agree a number are wary of breakaway regions: