Probably not... and I can tell you from my numerous experiments crashing and getting knocked out. The cheaper $30-40 helmets have so much mass that they usually don't shatter into many pieces. It's usually just 2-3 large cracks and there's enough material in the outer shell that it's bonded to to keep it together. On the lighter more aerodynamic road helmets, the vents are so massive that there's very little material in the webbing to keep it together. So when you crash, the helmet does indeed shatter into a bunch of pieces since the shell material is too insubstantial to keep it together. That's why they have to resort to an internal webbing of aramid, kevlar, or carbon fiber.

So the cheaper helmets use enough foam to keep itself together and the more expensive ones use an internal webbing of reinforcement. My guess is that the helmets in the $20-60 range can absorb more impact with the next strongest being the $150+ range helmets with the internal reinforcements and the ones from $60-150 (esp those towards the higher end of the range) are slightly weaker because they use less foam but also don't have the internal/external reinforcing.