Both signals will trigger if both areas are monitored, monitoring, in the same layers and looking at the same layers (mask).
If I look it like Tumiki Fighters ship pieces, I would make it in different layers and masks, and changing them on area_enter, and just base and attached monitoring for more (and with groups for filtering too).
You won't get immediate overlap information because there are many threaded steps between adding the nodes and getting them processed on the scene.
I have never used it (yet) but for that particular situation you can use Shape2D methods to get a simple quick overlap check between shapes:
ps: If this is the only time you will be checking overlaps, you may find a way to use shapes without Areas and getting a solution for your previous question ^_^
Look the "shower of bullets demo", uses an area for enter signals but if you dont need constant monitoring and other things provided by Area2D, may be what you are looking for
If you need shape's visual debug information, add a CollisionShape2D child to the area and add the same shape to it with set_shape, is the only way to get that, for now.