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Should we stay up all night, or not?
Literal
Night [object-を] see-through [whether-か否か].
A very short but register-heavy sentence. 夜を徹する ('to stay up all night,' 'to see the night through') is a formal/literary fixed expression. 徹する literally 'to pierce through, go all the way,' and 夜を徹する is idiomatic for 'to work/study/pursue an activity through the entire night.' The ending ~か否か ('whether or not X') is the highly formal, written equivalent of ~かどうか, mostly found in essays, legal writing, or classical-flavored prose. 否 (いな) is the classical 'no / nay,' preserved today only in set phrases like this one. Together the tiny sentence conveys 'to pull an all-nighter, or not' in a voice that sounds like an essay heading.