That's a hard argument. A few words added to a document like that isn't going to suddenly unravel potential DNA. If, for some reason, those few words caused a riot, or a revolt, or a coup, and so forth, then yes, I'd say those are sufficient butterfly-causing events to snuff a man out of existence 20-odd years hence.
The better argument would be whether the man would ever have become president. Or better yet, ignore the others and let's assume that during the mid-19th century that phrase was added via Amendment. Then your bland, blanket "butterflies" argument falls completely.
I'm sorry, nothing personal, it's just that argument is so wantonly flung on anything and everything without a little open-minded curiosity. This is AH.com, where anything alternative should get more than a single word dismissal.
Oh I can imagine how it could change things. Let's say that Republicans hurl impeachment charges against John Adams for maladminstration of the Alien Sedition Acts. And Federalists too for Jefferson's acts.
The mere word will change how politicians act, and while successful impeachment would be rare, let's say that Jacob Johnson would read a paper in 1808 calling for the impeachment of Jefferson for maladministration for the Embargo act. That paper would have a different headline in OTL.
It concerns him enough that when he made love to his wife, instead of Y chromosome, it was the X chromosome that reached the egg.
So in December 29, 1808, Andrea Johnson would be born.
Or let's just say, a supporter in North Carolina decided to go to Washington to express his support to Jefferson after hearing reports that some Federalists were attempting to impeach Jefferson for maladminstration because of the Embargo Act. He went to an inn in North Carolina on the way, where his presence caused hostler Jacob Johnson to delay his return to his house to tend to that supporter, whereas in OTL, he didn't. That delay was sufficient to change his lovemaking to his wife that she conceived a daughter. Or even a son, but with a different Y chromosome, leading to an Andrew Johnson with a different personality!
See?
And adding the word maladministration will be extremely difficult, as between 1804 and 1865, no amendment was added. If it was before 1808, then Johnson could be born a girl. If after, then you have to posit a scenario where that single word would be added, which is much harder than say, adding a word in the Constitutional Convention in 1787. The Democrats would see this as an attack of the Whigs to the legacy of the strong president Andrew Jackson, and will oppose it. Before his presidency, no president was worth having the word maladministration to impeach simply because usually, their party also controlled Congress.
Could you imagine a Federalist proposing an amendment to the constitution of the word maladministration in 1808? The Republicans would think of this as an attack on Jefferson, and it won't pass. If it happened during the Adams administration, same thing.
After the debacle of the election of 1800, it took a civil war to add another amendment. Why, because it removed a section that could block said passage of Amendment-the South.
I've already given my answer if the word was added. My answer? Not much, since the main obstacle to a successful impeachment is the 2/3 requirement in the Senate.
If all happens as OTL except the word, I doubt Andrew Johnson would be removed. Why? Ben Wade would become president! He actually didn't recuse himself, but sat in judgement in a trial that could make him president. Which made him unseemly, overly ambitious, and unethical to the other senators.
And a lot of senators believed Johnson guilty in OTL, but voted not guilty so as not to make Wade president. It would be the same. Misdemeanors, maladministration, they won't vote for Ben Wade to become president! It was 1868 anyway, and they knew Johnson would be out of office anyway with the election coming, so why risk the presidency of Ulysses S Grant by giving him a rival in Wade, and why give Wade the Presidency?
Ben Wade is one big obstacle in getting Johnson convicted, whatever the charges are.
It was said during that time that, "Andrew Johnson is innocent because Ben Wade is guilty of being his successor."