Comparing band-pass filters and convolutional kernels?
CNNs sort of irrelevant here because they are applicable when you have some invariant transform - shift or rotation. The idea of CNN is that weights are shared for different data points, not that weights are different. You are thinking about simple DNN. 

CNNs are also applied in speech recognition, but for a bit different task. For example, you can consider multiple frames jointly and tie filter shape for different frequencies. This way system learns Gabor-like filters. See Robust CNN-based Speech Recognition With Gabor Filter Kernels.

You can try to train your own kernels from raw data, they will eventually resemble bandpass filters. See Acoustic Modeling with Deep Neural Networks Using Raw Time Signal for LVCSR. This gives a marginal improvement.

You can also start from default bandpass filters as initial values and see if network learns an improved version.

You can also restrict network architecture to consider only the region around central frequency and just learn the weights in that region. Such network will unlikely improve anything.