EDIT: It does exist but is hardly "common"in AmE as the Webster's dictionary that Edwin Ashworth cited implies it is. It has not been used much since the mid 20th century in AmE (assuming the attestations on Google Books and internet searches are indicative) and many native speakers won't have encountered the phrase.
Original answer:
If it does or did exist, it is not in common use to be sure but is a rare bird. I've never encountered it, and I read through all 29 pages of search results for the phrase "as a man" and, unless I overlooked it, not one of the passages used the phrase in the sense A Dictionary of Confusable Phrases gives for it. Using it would only confuse 99% of your readers. The phrase that is in common use is as one, as WeatherVane remarked in a comment.
P.S. Still searching for attestations, I found one in "As Brave As Any Men Can Be" by Lieutenant Commander Burke Wilkinson, U. S. Naval Reserve (Inactive)
in the August 1950 Proceedings Vol. 76/8/570 of the US Naval Institute:
The Storting or Parliament slipped out of Oslo in the early hours of April 9. So did the King. The gold reserves of the nation were spirited away too, much to the fury of the conquerors. Oslo fell later that same day to paratrooper attack, made necessary after the seaborne operation had failed, and the world had warning of a new kind of warfare. In the afternoon the Storting met at the town of Hamar, with all but five members present. They voted as a man to continue the war—authorizing King and Cabinet to wage it from overseas if necessary. [emphasis mine]
and another in the Winnipeg Free Press Newspaper Archives for Feb 8, 1910:
This election they voted As a Man not for Tariff Reform or against free Trade but against the government which has dared to Lay its sacrilegious Hands on Trade ... [upper-casing in the original, apparently; I cannot access the full text as it is behind a pay-wall ]
and from the 1974 Manion Forum Yearbook [a conservative radio and television program hosted by Clarence Manion, former Dean of the Notre Dame Law School, from 1954 until his death in 1979]
Father Brown: ... the Christian Democrats did not elect Allende at that time, because their own candidate received 800,000 votes. But they did elect him in Congress. Being the majority party, they decided as a man to elect Allende over Alessandri.
and another dating from 1867 in the Proceedings of the Grand Commandery of Knights Templar and the Appendant Orders of the State of Missouri: From Its Organization in 1860 to the Proceedings of 1870 Inclusive (1885 reprint)
They rallied as a man to the defense of their principles and obligations and the Rite in this jurisdiction is comparatively dead.
I would still not call it "common". "as one", "as one man", and "to a man" are common.
Merriam-Webster offers this:
as one man
: with the agreement and consent of all : unanimously
"The council voted as one man."
P.P.S. Understanding the context of the citation is important for answering a question like this one. @EdwinAshworth and I have been discussing the value of attestation versus the editorial word of a dictionary. One of the attestations he mentioned in a comment dates from 2015, and it is one which I intentionally did not cite, but not because it seems to run counter to my argument; here it is:
"... Several men who worked on the Monon and New York Central Railroads back then were living in Medaryville and they decided, as a man, to pack up and go to Oregon. ..."
Here's why I didn't cite it. One might take it at first glance as evidence of normal current use in 2015. But it comes from a novel by Charlotte Lewis called The Secret of the River, and the phrase in question, as a man, is being spoken by a character, Mr Doyle, who in 2011, when the story is set, is an old man telling the history of the region during the 19th and early 20th century, and how a dam breach affected his own grandparents who were married there in 1907. Edwin himself says that the phrase as a man "probably has a literary / formal / old-fashioned flavour nowadays" and I think he is right about that. It is being put into Doyle's mouth as a form of characterization.