I'd say yes it is legitimate because the puppet itself is an individual object, even though it is made up of more than one piece of wood.
Otherwise you will require a group target for anything made up of multiple pieces of wood: a door, a table, a chair. This would invalidate a bunch of spells in the core rulebook (Pass the Unyielding Portal, Curse of Rotted Wood).
This in the face of the base individual being 'a plant' - so you're left with a choice. For me, it feels more appropriate to treat these manufactured objects as singular individuals.