No. A lot of “ADHD thing” tweets/memes are just quirks common across a wide spectrum of people. That they happen to also be common in those with ADHD is just coincidental.
For parentheses specifically, it’s just a personal writing habit, and there are other ways to communicate “a thought followed by a bonus thought” without having to use them — hell, parenthetical clauses themselves don’t have to use them. Parentheses in particular are probably a result of some people being taught that “a sentence is a complete thought”, which is a nice description for someone just learning grammar, but also not actually true.