Yeah, no. Subreddit mods can't do that, only the sitewide admins.
It's easy to prove this as anyone can create a new subreddit and see exactly what functions mods get. They don't get the ability to issue sitewide bans, only bans from their own subreddit.
Just waiting for Rocky to make a similar announcement.
Man, the nostalgia is real. It was Gopher and Usenet via CIX and Compuserve for me from around '88, and eventually "proper" dial-up via Demon Internet (in the UK) in '92. 9600 baud, 14k4, 28k8, 56k and eventually dual ISDN. I still have a 28k8 modem in a drawer in my PC parts graveyard.
Mods don't have any more ability to do it than any other user. They literally just have to use the "report user" function, same as anyone else on reddit. There's no secret special back door access to the admins that mods get. This is literally one of the things that mods complain about - they don't have any way to deal with ban avoidance and alt accounts except to hit "report" and cross their fingers.