Will Level 1 buildings under construction be active in the War Base?

All defensive towers are active in your war base, even if:

1. They're still being built (Level 0 to 1)
2. Being upgraded (they'll be at the level before the upgrade start)
3. Out of ammo (ie. X-Bows)

Answering your query about newly built towers that haven't been completed yet:
They'll function as normal, they'll be physically there (not leave any gaps) except only as Level 1.
I mean c'mon... Who's seen a Level 0 building?

Note: This only applies to newly built buildings... Or at least those that are under construction.
Cancellation of its construction will remove the building from your War base.