There is no built-in function.
You're using MonoGame, so you could just modify the MonoGame source to do exactly what you want.
You could also use reflection to get access to the internal
SpriteBatch member that holds the current count. In XNA it's the
spriteQueueCount field. MonoGame seems to be more complicated - look at the source code to determine what to reflect on.
Otherwise, the "nicest" thing to do, code-wise, would be to make a wrapper function for
Draw. Or simply manually increment your own counter every time you call
Note that this will give you the number of sprites drawn - which is not necessaraly the same as the number that appear "on screen".
If you're just trying to measure performance during development, it might be better to do something at the GPU level (I used to recommend PIX for this, with XNA on DirectX 9 - you'll have to figure out what works best for MonoGame on your target platform).