Hi!
No, there is no functionality built in OpenGL that handles this. That would be a higher level abstraction than what the API was designed to do. D3D doesn't do this either.
One solution is to simply add up all of the 'count' values from the draw commands per frame.
But this doesn't account for clipping/culling so I suggest using a debugging/profiling tool such as AMD's own PerfStudio2 or Intel's Graphics Performance Toolkit or similar.