It doesn’t seem like it - JKR says the curse broke after his death.
From what J.K. Rowling says in an interview, the curse was broken after the Dark Lord died.
MV: Do you-- do Ron and Hermione or Harry ever return to Hogwarts in any capacity?
JKR: Well, I can well imagine Harry returning to give the odd talk on-- on Defense Against the Dark Arts. And-- I-- and, of course, the jinx is broken now because Voldemort's gone. Now they can keep a good Defense Against the Dark Arts teacher from here on in. So that aspect of the-of the wizarding education is now provided for.
- Today Show interview (July 26, 2007)
This implies he either didn’t try, or was unsuccessful in, removing the curse on the Defense Against the Dark Arts job, since it only broke after his death, not after he took over Hogwarts and put Amycus Carrow as its teacher. However, we don’t know whether he didn’t try or was unable to remove it. It’s also possible that he didn’t intentionally or knowingly curse the Defense Against the Dark Arts teaching post, but that his anger at not getting it caused ‘accidental’ magic to curse it, which would explain why he’s so willing to put his servants (Quirrell, Barty Crouch Jr., and Amycus Carrow) in the position, and why he never used a similar curse again.
It’s unclear if it’d affect Amycus anyway - he taught Dark Arts.
Whether or not the curse would have affected Amycus Carrow is unclear - he taught Dark Arts, not Defense Against the Dark Arts. The subject became the opposite of what it originally was, and not knowing exactly how the curse worked, it’s impossible to say for sure if it’d affect Amycus or if it’d consider the Defense Against the Dark Arts teacher post empty, since no one actually taught that.
“Amycus, the bloke, he teaches what used to be Defence Against the Dark Arts, except now it’s just the Dark Arts. We’re supposed to practise the Cruciatus Curse on people who’ve earned detentions –”
- Harry Potter and the Deathly Hallows, Chapter 29 (The Lost Diadem)
If it was an intentional curse, it’s possible that the Dark Lord knew it wouldn’t affect the Dark Arts teacher, so he wouldn’t need to remove it. However, we don’t actually know if the curse affected Amycus, or very much about how it worked, other than making the Defense Against the Dark Arts teacher leave within a year, requiring Dumbledore to hire a new one every year.