If a druid were to pick up a wooden table leg used as an improvised club, or a tree branch small enough to be wielded as an improvised quarterstaff, could the druid use the shillelagh cantrip on the improvised club or quarterstaff?
The shillelagh spell description says:
The wood of a club or quarterstaff you are holding is imbued with nature’s power. For the duration, you can use your spellcasting ability instead of Strength for the attack and damage rolls of melee attacks using that weapon, and the weapon's damage die becomes a d8. The weapon also becomes magical, if it isn’t already. The spell ends if you cast it again or if you let go of the weapon.
The spell description restricts the cantrip to clubs and quarterstaffs that are wooden, but says nothing about improvised clubs or quarterstaffs. If a weapon is improvised as either of those two weapons, and is also made of wood, might this cantrip be applied to the objects in question?