The short answer is yes! Here's the breakdown:
Shootout abilities you use must come from either an action card in your play hand (which is played and then discarded), a deed, an Improvement (a card with this keyword), your outfit, or a card in your posse (i.e. a dude or one of their attached cards). You can also use a Shootout ability on a card that’s not in a posse, but only if that ability would bring a card currently in play into a posse.
Shootout: One or more of your Deputies in any location(s) joins your posse at a Government deed (moving if necessary).
As Rafi satisfied the last sentence regarding shootout abilities, he does not have to be in the posse and can choose not to move himself in as part of the action, sending other deputies into the fray!