It's decent logic. If we're trying to keep good people alive primarily, then a random lynch on day one makes no sense, it's just an avoidable risk.. assuming there's enough people in the fellowship to last the 7 days (if, worst case scenario, one per night died). Depends how many the mafia/gollum kill each night too, or if Gollum obtains the ring, like was suggested earlier. If that happened, not using the day phase at all would mean we had very slim chances of winning. It's all ifs though, and i agree that a random lynch, particularly on the first day in this particular game, would be unwise.
So, i'm going to also vote: no lynch
assuming we're allowed obviously.
And i do know where everyone else is coming from as well, as usually i'd be all for getting the information. But it's a different mindset when all we really have to do is get one of 4 people (i presume we have 4 hobbits) to survive 7 days. There's just as much chance of killing one of those as killing mafia, which would be more harmful than the small amount of information we gained would be beneficial, in my opinion.