No thanks to the pet. The background story in XI for a wyvern worked well enough, but XIV's lore and Ishgardian history is already well enough established, and it doesn't look like a map re-design is going to throw that out the window.

...not to mention that etymologically, "Dragoons" were mounted infantry. Nothing more. If they're eventually working to include fighting alongside (and possibly even on) mounts in the future, then that base will be covered.