This is generally not true.

A pointy triangle could be idealized as an edge, the resulting circle will always be bigger than a bounding box.

(The corners of the box are on the circle, see Thales's theorem)

You might now claim that something like a regular octagon is better represented by a circle (probably).

But how does the average polygon look like?

I bet it depends on the randomization

• random vertices
• random edges
• random angles

Furthermore it'll be more difficult to fit circles into a quadtree search.

I think using circles in a Cartesian system causes too many headaches.