I had not read far enough in the thread to realize this was about a non-dedicated flash. I do think compatibility is not the right word concerning them, in that manual flashes are rarely dedicated (for Nikon or Canon, etc). They are still compatible, they work OK - just like studio flash are not dedicated either (and they certainly are "compatible") But manual flash only use the one center pin to trigger them, which is all a radio trigger, PC sync cord, or optical slave can use. There is no other communication with the camera.
But to be detected present on the camera, a flash today on a Nikon would need to be a CLS system flash, communicating with the camera (the other three pins in hot shoe), which could then be sensed present, and could communicate the Ready light, and it could even show ISO and fstop values for example. None of which affects how a manual flash works. More is an unnecessary function on the flash. More communication could be convenient to the camera automation however, to at least know the flash was present. But almost all manual flashes are non-dedicated.
I could add that a manual flash really needs a manual camera too. For example, we absolutely have to turn Auto ISO off - we can't have the camera changing ISO after we get the manual flash power set up. And we have to use camera M or A mode, we cannot have S or P modes changing aperture after we get the manual flash set up.
Regarding shutter speed itself, the flash could not care less what it is, since shutter speed does not affect flash exposure. So we can set shutter speed any way we wish, except we must not let the shutter speed exceed Maximum Shutter Sync speed (often 1/200 second). If it were a system flash that the camera could detect present, the camera automation would not allow the shutter speed to exceed the Maximum Sync Speed.