Is there any record of people in the year 1234 noting the unique consecutive nature of it?

by DontPoopInThere
DerbyTho

You might be interested in this answer from the FAQ where u/sunagainstgold notes that in the high Middle Ages (the time you are asking about), while chroniclers like Herman of Reichanau are numbering their entries by A.D. year, we're not quite at the point where it’s common usage in charters or in people's minds.

That's not to say there won't be any people noting it, of course!