Question: Would one say, "I'm going to add a 20 days notice on file", or I'm going to place a 20 day notice on the file. Does using "A" merit the change of days to day? Even when 20 is plural, does this happen?

Answer: The "a" has to do with the word "notice", not the 20 days.  Accepted usage is "a 20 day notice".  Your second choice is correct.
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