Oh for sure. But I think this explains a lot of the misunderstandings between Scottish polity and that of the rest of GB, which have resulted in (thus far) 45% of the Scottish electorate voting to break away. Both sides of the political relationship have a very different understanding of what it is and don't really understand that this is the case. The phrase 'the Union' is basically never used south of the Tweed for instance. Or consider the Thatcher government: there was genuinely no awareness at all that making the Scottish Secretary the Government's Man In Scotland (rather than Scotland's Man In The Government) would be seen as breaching a constitutional convention.
Absolutely, politically, the concepts of Britishness/The Union as 'personal-political' was initially a contrast to 'Irishness', (in that being a unionist was more 'Irish' than being a nationalist) Certainly the migration of Ulster protestants to (or in some cases back) to the Scottish cities in particular at the start of the last century brought that into the Scottish political scene. The imagery, and the rhetoric was easily re-orientated for nationalistic purposes of a different nature during the two wars (and in the National Government)
In Scotland, we got the Unionist Party (in which 'The Union' was interchangeable with the concept of Empire and most importantly with strong industry) Indeed it was a Scotsman's
duty to be a Unionist as it promoted 'Scottishness' within the Empire where you could be
as Scottish in Australia/New Zealand/Canada etc or in a mine in Yorkshire as you were in Scotland.
As Tories and Unionists became Conservatives they had a well from which to draw in order to establish a concept of Britishness and of 'The Union' out of what was left of the Empire. This was done in many cases to try and take something tangible
into Europe. You had to get from Empire (which didn't draw from mid 1800's romantic nationalism) to 'Great Britain' in less than 20 years.
Being in Europe has made Great Britain an entity (flegs, queen, curries, Jessica Ennis) and keeps it that way. This is what those who campaign for Leave can't grasp. British identity doesn't exist without Europe.
There is a sense of the need to be 'interconnected' in Scotland, as it was with the Empire (see emigration) it's now with Europe. It's a genuine 'thing' that really requires more academic study and isn't just an 'oh the Scots like to think they are x' diagnosis that is often made when faced with whether there's a 'Scottish exceptionalism' with respect to the left-right scale, perceived social liberalism/secularism etc.
The Union guaranteed these things. The threat of not being in Europe is the key determiner of what 10% of the Scottish electorate are going to think with respect to their constitutional future.
I don't think the threat to revisit the constitutional question in the near future is an idle one with respect to the outcome of the EU referendum.