If it is the Spectre it would probably be the leader, yes. The last time I tried running a game like this, the Spectre was the "leader" but encouraged the rest of the team to show initiative and make plans themselves, since that was part of their test as Spectre candidates - basically he was Nihlus if Nihlus had lived. That seems like a good approach to me, though of course a different Spectre might always have chosen to pull rank instead.

The stats would be arranged as proper RP stats in the end anyway. :P The prose write-up is mostly for fun, and I guess it could be easier for some people to make a character like that. That being said, I would require brief appearance and backstory write-ups in addition to the character sheet itself either way. It's easier to extract plot hooks from a backstory, and appearance helps visualise whatever is happening with the characters.

EDIT: Also, yes, not having Spectre authority would probably force you to tread more lightly and be more sneaky. On the other hand, it'd also help keep a low profile.