Hyuran Ishgardians exist, though I would imagine ones held in high esteem or "highborn" would be very rare as Ishgard was and is still a steadfastly Elezen city-state to this day.
Heroic actions can lead to an elevated status in life (this is hinted at in the MSQ) but the fact remains that the High Houses and many of the highborn in the city seem to be almost exclusively Elezen. A Hyur is likely faced with an unbreakable glass ceiling in life as an Ishgardian.
The title of "Dragoon" is awarded to soldiers who have a confirmed kill of a dragon, which is usually those who have trained in the lancer arts and are able to use Jump techniques. A WAR/PLD can technically be a "Dragoon" but it is in title only.
Generally speaking, an Ishgardian laying with a non-Ishgardian of any race is considered taboo. I can't see why an Au Ra would be any worse or better, depending on exactly how draconic their heritage is.
This is a major point of contention for most people. Some don't mind IC Fantasia, some loathe the idea, and some (like me) are generally ambivalent provided the reasoning and handling of it is sound. It all boils down to whether or not the people you will be RPing with most of the time can stomach it.
I... can't say I'd ever want to claim someone being Fantasia'd as a baby, because that seems terribly irresponsible and neglectful, but again, it's up to you and the people you RP with.