You may be correct, but my reading of Rule 3 differs:
(B) A player who has not previously contracted with a Major
or Minor League Club, who is not a resident of the United States
or Canada, and who is not subject to the High School, College or
Junior College Rules, may be signed to a contract if the player:
(i) is at least 17 years old at the time of signing, or
(ii) is 16 at the time of signing, but will attain age 17 prior
to September 1 of the calendar year the player signs the
contract.
I think this is pretty clear. A player who is 16, but will turn 17 prior to September 1st, may be signed at age 16 - i.e., on January 15th.
A player who turns 17 after August 31st may sign as of the time he turns 17 - i.e., sometime in the fall.
The relevant word in the rule is the last word in subsection (i). That word is "or."
The point of the rule is that a player may not be signed at age 16, unless he will turn 17 during the regular minor league season. But there's nothing there that prohibits signing a player on his 17th birthday, if that birthday is December 1st.
Now that said, the Phillies, at least, have not signed an international amateur free agent later than sometime in August, for the past several years (they did, several times, in 2022 and earlier years). It may well be that clubs just don't, as an unwritten understanding with the last rule change; but I see nothing in the current Major League Rules, or the relevant attachment (#46) to the Basic Agreement that would prohibit such a signing.
It's probably not relevant, anyway.