Absolutely baseless speculation: I'm guessing it will work asynchronously like you're describing. My reasoning being that if it's you + five friends, you can't include everyone in a fireteam (or whatever we're calling them in this game), meaning if everyone's online and available, someone's going to get left out, which isn't a good feeling. Plus, if we compare to Destiny's (admittedly flawed) clan system, you've got a system where individuals can contribute to the group through solo play (when they bother to give us solo-able bounties, at least), so there's precedent in the genre.
Baseless no more! Async for sure. It doesn't matter who plays with who, just that they play at all.