The outcome of the Supreme court judgement will revolve entirely around what fresh material may be uncovered by the enforced release of material by the Parliamentary request. I doubt any private communications will be released as this would be in breach of EU law on data protection.
The Independent sets it out thus:
Only a summary of the Scottish Court’s reasoning has been released, with the full judgment to follow on Friday. Meanwhile the High Court in London has today released its reasons for rejecting Gina Miller and John Major’s legal challenge to prorogation. Its judgment is a powerful restatement of the orthodox legal view, and firmly and rightly rejects the constitutionally dubious argument that parliamentary sovereignty permits or requires the courts ‘to exercise hitherto unidentified power over the Executive branch of the state in its dealings with Parliament.’ The circumstances and reasons for proroguing Parliament are for the Government to decide.

The Government is bound by law in Scotland and Northern Ireland, just as much as in England and Wales, which is partly why litigation was commenced in all three places. It will now be for the Supreme Court, which hears an appeal on Tuesday, to decide whether the advice to prorogue Parliament is for the courts to decide and, if it is, whether Tuesday’s prorogation was unlawful.