Doubtful. Back in the day when my 'work computer' was a Pentium (Pentium 200MMX to be exact) playing a MP3 consumed 50% CPU. Note, I no longer remember if mpg123 was using MMX instructions or not.
Given how much faster a Pentium 200MMX was than any 386 CPU, I very much doubt a 386 (even a DX) would have had enough power to decode in real time a MP3.