Nope. While it's true that hot air that has already radiated can be pushed out by cooler air moving in naturally more easily since there is nothing to trap it, closed systems that channel all the available ambient airflow over and around components will aid in removing radiated heat much better as the pressure and movement are not mitigated by the enclosure being open which allows much of the airflow to go places OTHER than where you want it to. Chiefly, over and around components instead of just out the top of the case or with no case, just wherever there is no resistance to it going.
Consider, a room fan blowing through a 24" piece of pipe from 5' away will have far greater force and cool your face much more effectively on a hot day than one that is five feet away and is just randomly blowing in all directions with only a portion of it actually making it's way to where you are on the couch, again 5' away. At a smaller scale it's not much different with an closed, somewhat pressure differential configured enclosure.
For CPU and GPU coolers, which have their own fans to remove radiated or conducted heat away from the heatsink, this is not as big a factor however for motherboards, drives and the areas of CPU heatsinks and GPU components that are not directly cooled by it's heatsink, that air moving through the case that flows directly over those areas tends to offer additional cooling that you would not see on an open air case.
I've seen test results going both ways, but in my own investigations I have always seen lower overall temps with a closed case that has very good cooling than when I open the unit up and turn it on it's side so that nothing is trapped inside. I'm convinced that direct airflow provided by good air movement is more effective than a passively open case where most of the fan pressure simply escapes and does not go where you would prefer that it went, mainly, over those areas I described plus the memory modules and any other hardware that may be in the case like controllers or lighting (Even though heat is very minimal these days from lighting since most are LED).
If open case passively radiated configurations worked better, we would not use fans at all. And if the case is open, the case fans have very little impact on cooling anything except those that are directly mounted to something you are trying to cool.
Now on cases with poor case cooling, open would definitely be better. No question.