Yea the connection with the GOVERNMENT is still possible, there's writing for that already laid down Oda can build upon. However, him being some Marine admiral (especially when he'd barely be 30 years old) doesn't make sense. I think either CP1-9 or CP0 would be the best fits. We already know he started his anti-WG shit by the time of Roger's excuetion (had already started wearing his green cowl). And then starting the army post-Ohara now.
What is your backstory regarding him, if we remove the WG connection?
The main points that cloud his characters in my view are:
1. Dragon having a major secret regarding his past.
2. Secrecy in general is not a trait you find in his family. To think that even his most trusted subordinates don't know which sea he hails from
3. "Dragon" has to be the most edgy name in the manga, I can't fathom Garp naming his son that name lol
Two possibilities regarding his origins, he's either not Garp's son to begin with but held his wife's name for secrecy purposes (very low chance) or his mother was a very special person, potentially an exiled celestial dragon? adds up well with Garp's detest towards them
As for what he was doing, it's hard to imagine him being a pirate "A pirate eh? Not a bad idea"
Affiliation with the WG is the most reasonable guess, especially since he knew Vegapunk.