NJ, picture this possibility (already indicated in more than one AB thread on the subject):
May is seen to be high handed and, as a result (in the eyes of those who want it), going ahead with a referendum vote is even more pressing. Those who up to this point were undecided then take the view that they agree, Westminster (in the person of Mrs May) IS high handed and even arrogant (never mind those who hold tightly onto "the constitution of the UK" and harrumph on the point) and join in the support for independence. As the polls show the swing past 50% support for independence we would no doubt get a repeat attack of incontinence in Westminster and a rush to intimidate/frighten/promise Scotland anything and everything, "just don't choose to leave the UK". Compared with the earlier referendum, overall more than 5% of those who vote move to the independence side and the referendum ends in a vote for independence.
How much ice do you think it would then cut to say the vote was invalid/meaningless/etc. because "it is illegal according to UK law" since it was not "authorised" by Westminster ?
When Southern Rhodesia declared UDI the UK garnered international support within the UN and elsewhere, condemning the move as illegal - but the UK did not send troops to put its colony in its place. A civil war ensued and white rule ultimately was swept aside with at most indirect UK involvement. I don't think the UN would be consulted nor would there be (any) international condemnation or even criticism of Scotland's choice/decision (there would very possibly be indications of support and quiet advice that Westminster accept).
The UK moved militarily against its fellow NATO founding member on the basis that it was "contrary to international law" for Iceland to extend its jurisdiction/control of fishing to wider limits, and not just once. The UK's stance did not garner significant international support (although NATO's failure to move to mediate was starkly notable). These were episodes that the UK would dearly like to forget and fortunately the Icelanders are not vindictive but quite forgiving (let's not go into Brown/Darling's shameful treatment of Iceland in 2008 and beyond, which also seems to have been quietly forgiven).
And, note, Iceland was a hesitant world's first country to recognise Estonia, Latvia and Lithuania as independent countries following their declaration(s) - might they repeat in Scotland's case ?. Would Westminster not want to lead with its blessing rather than (again) look less than magnanimous or even statesmanlike ?
Would Westminster send in the troops to seal off Holyrood ? Would there be arrests of "separatists ? I don't think so. I think there would be a frosty few days, maybe a week or two, while No.10 et al decided what they could do - but then there would be a move to "gain the moral high ground" (with a firm eye on the media after the storm following the result when Westminster's position was worse than the Queen's was in the immediate aftermath of Diana's death) and a flurry of statements will emerge: "....hear the will of Scotland....", "....congratulate the winning side....", "....wish Scotland well....", "....will of course work with Holyrood to make this work.....".
In the cold light of such a dawn the "constitutional aspects" will, I suspect, be what becomes utterly irrelevant.