It's possible that Paul is alluding to that verse in Isaiah (small correction though - it's 33:18 and not 34:18). Apart from the repetition of "Where is the scribe?", the structure of the two verses is remarkably similar, with their series of "Where is ..." questions. However, I don't think he's directly quoting it (apart from maybe that one part about the scribe). Admittedly, with the New Testament being written in Greek, citations from the Old Testament are really Greek translations of the Hebrew in which the OT was written. That's why the English translations can end up looking a little different when you compare the Old Testament originals with their quotations in the New Testament. (God knew what He was doing with that though.) Even taking that into account though, I think Paul is, at most, alluding to the Isaiah verse and not quoting it in full.
Verse 19 of 1 Corinthians 1 does appear to be clearly referencing a verse in Isaiah though:
Therefore, behold, I will proceed to do a marvellous work among this people, even a marvellous work and a wonder: for the wisdom of their wise men shall perish, and the understanding of their prudent men shall be hid. (Isaiah 29:14)
So it's not beyond the realms of possibility that Verse 20 might be hearkening back to Isaiah 33:18. In any case, the phrase "Where is the scribe?" only appears twice in the KJV. Based on that, I would say it wasn't a common question.