To answer the question more bluntly...in a word, NO.
If DSP means those church, jazz pub and arena sound field modes that are simply reverb and equalizing functons, it's not necessary. In fact, they should be avoided at all cost when watching on your HT. But for sound-only stereo sources, they can impart some novelty to the listening experience, although I also prefer unadulterated pass-throughs.
But these days, DSP can be your entire AVreceiver already, after the decoder chip, especially if you invoke such features as Audessy which equalizes the LPCM data across all your speakers depending on your room accoustics or when converting stereo to Prologic. DSP, afterall, stands for Digital Sound Processing. So that any kind of manipulation on the digital audio stream (LPCM) prior to D/A conversion can be called DSP.