Quite! Where's the fun in that?
I for one in my years of doing exactly as the OP proposes, have never had an issue - staff don't bat an eyelid.
It was even more common in the days before the Edinburgh-Glasgow was electrified, as First Class fitted 170s would also appear on Anniesland, Alloa and Dunblane workings - which were all Std only. I believe the Edinburgh to Dundees did officially convey First Class then, as did most Edinburgh to Perths, but that hasn't been the case for a few years now and the GBTT data makes it clear these services are Std only.
(You can look them up on National Rail Enquiries and they are shown as Stanndard Class only.)