I can't wrap my head around this. Is it legal for parent nodes to contain additional logic ?
It wouldn't really make sense. Behavior trees have their conditionals at the leaf nodes. Those conditionals determine if the traversal will continue to the other leaf nodes in that parent, or move back up to the other parent nodes.
You seem to be talking more about decision trees, where it's expected to have logic in the parent nodes.
You can learn more about the two here: Decision Tree vs Behavior Tree
Further, just because it's not the standard way it's done, if you have the situation where you want to create this new data structure that has conditionals in the parent nodes of a behavior tree, go ahead and do it. Game design is a pretty "open to interpretation" kind of thing, so just do what works for you.