Musashi:
Is that how others would view the role/place of a monk in this situation?
I don't think there are any straightforward answers here. Honestly, monks shouldn't be in this situation. Joining a monastic order (I'm excluding the tattooed orders for this purpose, even if they are monks) pretty much means severing all ties with your life as a samurai, serving a Clan. Monks can certainly be welcomed and even sought out for their insight and advice, but I don't see them being asked to become involved in Clan affairs - maybe if those involved family members of the monk or there is some other, similarly pressing reason, but those would be extremely rare cases, I feel.
That said, the situation is what it is so there's no point in agonizing over what could/would/should be. The most probable reason why Musashi would be present is to allow for the point of view of one who is less biased and who can offer insights a samurai might not understand. Secondly, a more sly reason, Kuwanan might feel there is an advantage to be gained from adding an unknown element to his task force: monks are treated differently and provoke different reactions than samurai. Either way though, Musashi is present because he was invited to be. To me, that means his input will be appreciated and even expected. I don't think Musashi should necessarily sit there quietly and not involve himself.