The short answer is no, but it’s certainly not impossible. Todoroki is a fairly common family name in Japan. The tanto that Dabi wields could be his only way of answering the question since he doesn’t really have many ways to speak his thoughts out loud during an interview. Or, if you take any of the routes that make him a terrorist or a part of a government organization, having connections to the Todoroki family would be quite easy.
There’s no particular evidence in either Boku No Hero Academia or My Hero Academia: Vigilantes that suggests he has any type of connection to them whatsoever, but it still is very feasible. I hope this helped clear things up for those who were wondering!