Is it advisable to wait to unbox my new iPhone?

You don't have to open it, but you only have 14 days from purchase to decide whether you want to keep it or not.

When Apple's holiday policies kick in, usually in early November, you will have until early January to decide.

Returns & Refunds - Shopping Help - Apple

No, it shouldn't affect your battery life.

It's no different than if Apple ships a store phones and they don't sell for a month or two.