Are buildings currently being upgraded able to function during clan war?

My clan has been in wars since the Clan War update, and I can give a more complete answer with regards to the most current update as of February 2015.

All buildings - defensive, offensive, town hall, any except clan castle - will be reflected in your war base at their highest COMPLETED level, all the way to the end of Prep Day. Once Prep Day ends, your entire war base is set in stone. This means that if you started a L3 Xbow, but it will not finish until after Prep Day is over, it will remain at L2 in your war base, unless you decide to finish it early with gems.. in which case it would be L3 for war.

NEW structures that you start building before or during Prep Day will be automatically included in your war base at L1 - even if they are still unfinished in your normal base - provided you edit your war base and place them in time. This is especially important for new town halls. For example, if you finish a L9 town hall during Prep Day, you could start your 2 new Xbows, air defenses, archer tower, etc.. and they will all be available to be placed in your war base at L1, even if they are still under construction when Prep Day ends.

Town hall upgrades completed during Prep Day will also show up now on the clan war base map. However, upgraded clan castles will NOT reflect their new, higher troop capacity, unless it finishes BEFORE Prep Day begins. That is the only exception I am aware of to date. But overall, upgrading bases are more fluid than ever until Battle Day.