No?

You will have the same chance at night of losing someone regardless if you lynch day one or not. If you don't lynch day one, you only lose 1 person verse losing possibly 2.

We may be lucky and a night kill may not go through. That's up to chance though. We can't control night one's chance. We can control day 1 though. Why not keep more of us alive rather than sacrificing someone? We don't have that much information to go off of on day 1.

I would feel more comfortable keeping a possible useful town role(or two apparently) alive then losing two people from Day one and night 1. Which could possibly be 4 useful roles with this new info!