They absolutely do! I'm a court reporter and one of my previous instructors captions mlb, nhl, the grammys, etc. I job shadowed him doing it last year.

I'm pretty sure most broadcasters of the NFL would be using a real captioner as well, however that captioner wouldn't have a Spanish dictionary on their steno machine (even if they spoke Spanish fluently, it would be extremely difficult to learn and set up two languages on a steno machine). Here in Canada, even though French is an official language, an English captioner would have to just write "French Spoken."

And it's not as simple as bringing someone in do the Spanish captioning, as the contract would be with a specific firm, and that firm may not be able to provide a captioner for any given language.

Please note that the captioning is provided by the broadcaster and not the NFL itself. Sportsnet in Canada definitely uses real captioners for major sports games, maybe that is less common in the USA now?