The case is also going to radiate heat and turning it upside down will make that less efficient. The base won't radiate heat in the same due to being plastic and due to it already being used to pass air through.
The case isn't thermally connected to the SoC in any direct way, so while I'm sure it does radiate some heat, I think it's pretty negligible. The PSU sits at the "top" (in regular orientation), and I don't think it runs much of a risk of overheating.