Is there a way to pragmatically determine if a braille display is connected to iOS?
There are changes I want to make to improve the experience for those users if I know they are using braille instead of audio VoiceOver.
"Improving" user experience for a specific AT is almost always a bad practice. Separate is not equal. If there is a scenario in which you don't end up with equality, adjustments are fine, but these adjustments should typically take place as part of the AT or OS and not the job of the application developer.
I don't believe the APIs support this, and if they did I would recommend against it in almost all situations, especially if you're an accessibility novice.