If one is more interested in understanding how algorithms in the biological brain solve problems (theoretically, particularly the mathematical aspect), and possibly in building brain-inspired computation (applied theory, particularly neurorobotics), then is it suggested to focus more on studying computational neuroscience rather than artificial neural nets/machine learning? It seems the latter one is more oriented toward any algorithms just to solve problems via computer simulations without the constraints of biological brains, though there are still large areas for theory of machine learning and artificial neural nets.
Computational neuroscience and neural networks are both studied on this MSc at the University of Sussex. When I took the course in 2004/5, the Neural Networks module was compulsory, and the Computational Neuroscience was optional in the 2nd semester, so that would suggest the course designers (world leaders in biologically inspired computing) thought that studying neural networks first might aid the study of computational neuroscience. I think some of the other subjects taught on the course would be of interest to you, e.g. evolving genetic algorithms for robot control (see Rodney Brooks – and the iRobot corporation).
Lastly to answer the question(!), I think you probably need some understanding of (simple) neural networks (artificial or otherwise) to understand more in-depth concepts in computational neuroscience.