His "symbol" is the flag of the old world. Of course it's everywhere in Big Mountain.
I believe he was refering to the marking placed at certain locations where supply stashes can be found its an actual hand drawn mark of the old world flag facing downward.
Tel Prydain Posted Ulysses was a cut companion, and obviously there is his house in New Vegas.Since he used to be in the main game there will be quests that cross between LR and the main game.
Theres no reason to think any quests will cross or that wolfhorn ranch which was to be his home has any real meaning now he was cut and most likely altered from his original concept much like the elements fron Van Buren where Graham is a far cry from who he was in the Van Buren design documents so its very likel that Ulysses was also changed.Also the base game and dlc can't interact so at most we'd get a few lines of dialouge mentioning things in the Mojave that would be the same regardless of allegiance or quest completion.