Audio DSP for hobbyists
No, you can start DSP with C, Matlab, or Octave to name just a few. DSP is mainly about filtering, but also about signal processing and algorithms to  manipulate sampled signals in the time and frequency domain. A beginner could learn how to implement filters and also spectral estimation. There are also algorithms to detect\generate tones and chords which might be of interest for audio hobbyists. All you need is some sampled data to play with and a way to manipulate that data, the rest is learning about the math (google is your friend). 

Real time DSP involves making these processes run fast in an FPGA or DSP processor, which you would need hardware for. I had some labs once where we built adaptive IIR filters that would filter out a tone real time from audio with only a few msecs of delay. We implemented and tested the filters in C and Matlab before implementing them in hardware.