It’s very likely specified as an acyclic graph (because, without checking, I see no reason why it would not be). So if you made a cyclic graph it would be wrong. It’s possible, likely even, that a lot of git’s implementation and associated tools don’t check for that, because it’s very hard[1] to achieve, but that just means stuff would break in more non-obvious ways.

[1] Constructing a cyclic git graph means finding a hash collision, and git uses SHA1 which is known to have weaknesses. With another hash algorithm it might be “practically impossible” instead of “very hard”.

You can use the "grafting" feature to emulate rewriting commit parents (but not true rewrite--as in the object itself is not actually modified and some tools do not respect it), so maybe give it a shot