Nope, roster-wide buffs are only applied when the character is in the active roster. Most of the traits are unstackable, with one exception - Omen. I've also updated the visuals and the day-end screen in the 0.2 update to help players better understand how everything works. You can check it out on Patreon (it's free). I'm just afraid to upload it here for now because I don't want it to get delisted again.