It is not a common word in any register. In Goodbye to All That Robert Graves tells a story about T.E.Lawrence which illustrates this point:
Professor Edgeworth, of All Souls’, avoided conversational English, persistently using words and phrases that one expects to meet only in books. One evening, Lawrence returned from a visit to London, and Edgeworth met him at the gate. 'Was it very caliginous in the Metropolis?'
'Somewhat caliginous, but not altogether inspissated', Lawrence replied gravely.
I am pretty widely read, and I have never encountered the word outside this context.