You can roleplay anything within reason in downtime. There is nothing really stopping you doing this roleplay in person at a player event, whether or not it is sanctioned.
(In practice, “sanctioned” really just means “plot approved by PD” and “follows the Empire rules, including Conduct”.)
So you can absolutely have a fight as your characters. As you’re not at a mainline event, there won’t necessarily be any refs around to ensure fair play and safe fighting - that’s on you. But you can treat the outcome as canon as long as it doesn’t go against PD rules or established canon.
So you can have a winner - you can give out your own prizes - you can even have someone die. But their death can only be self-reported the same way any player can self-report character death on the website.
Breaches of the conduct rules could have an impact that would be picked up at a mainline event. This might extend to massively unsafe fighting or intimidation of players
But otherwise, PD have absolutely no power to stop you fighting with foam swords in your back garden.