Apparently, they do. Per the FCC website, they state:
“Subtitles in Lieu of Captioning
The rules provide that open captioning or subtitles in the language of the target audience may be used in lieu of closed captioning.”
So if you have a program in English that is being broadcast on a Spanish-language station intended for a Spanish-speaking audience, having this program with translated Spanish subtitles would fulfill the FCC requirement. Also, subtitles or open captions for the deaf and hard of hearing in English, would also suffice. It is up the producer of the show if they want the open captions or the subtitles to always be on the screen, or if they prefer that the viewer have the option to turn them on or off.