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.

For upgrades, if the upgrade will finish before war ends, your upgraded level will show up in war base.