I highly highly doubt it. It is really good for the main thing it is designed for: language and translation. And because of it's function it can hallucinate for you decent code or answers to basic issues.

Try something, I've done this personally. Go to any of the big "AI" models right now. In another tab, open up the NYT games, letter boxed. Now try and teach the "AI" to play letter boxed. It isn't a complicated game but the few restrictions you do have are hard restrictions. For a language model coming up with words that fit the restriction and giving you a solution should be pretty straightforward if it is truly smart. Just a list of a few words that meet the criteria of the game that will solve today's puzzle is all it needs to do. Do it. See what happens.

EDIT: Been a few weeks since I last tried. Just tested it on 3 big models. All failed. The answers almost look right for some of them. But they fail. Here was my input:

You will solve a word puzzle. All rules must be followed all the time.

There will be four arrays of letters labelled 1, 2, 3, 4.
The first word may start with any letter from any of the arrays.
A word must be in the English language.
A word can contain more than one letter from any array.
A word can not contain two letters next to each other from the same array.
A word may not contain the same two letters next to each other.
After the first word is chosen the next word must contain the last letter of the previous word.
All letters from the arrays must be used at least once.
A solution should contain less than 5 words.

1: E, T, N;
2: O, S, B;
3: W, H, U;
4: V, A, L;

Solve this word puzzle using the rules and letter arrays as stated.