Allegiance question

At this moment. No.

It just a big PvP game mode.

Yes, you can vote up hourglass(and hope to not get invaded), then put loot on your ship. The treasure class will rank up and max out at grade 5. Then you lower hourglass and you’ll get allegiance. It’s not a lot but definitely higher than the amount gained from a loss.

I believe you can collect treasure before voting up hourglass and keep it on a rowboat. Then once you vote up hourglass, attach the rowboat and you hit a high treasure class. The amount goes up once it’s on your ship. However, if you put treasure on your ship before voting up HG, the treasure class won’t go up.

Another way to gain allegiance is turning in flags. If you can obtain reaper flags, from finding them in the water or sinking a ship on adventure, you can save them for a quick turn in.
Head to an outpost, vote up Athena emissary, vote up Guardians hourglass on your ship, then turn in the flags. You’ll gain allegiance. This also works with Servants and all flags. NOTE Once you vote up Hourglass, you cannot vote it back down for 15 minutes. So be ready for a quick invasion. But if you’d like to start a quick pirates life tall tale, heading through the portal may help shorten the timer 😉