Yes. Since you don't have much choice, the best way is to drop the microcontroller idea and make use of the PC's powerful processor and plentiful RAM. You'll have more libraries to work with too. However, you may retain the microcontroller solely for the purpose of data acquisition and data transfer.
The main problem with microcontrollers in speech processing is not only their lack of multipliers, but more importantly, their limited RAM. Higher-end PICs give you 4kB of memory. But the human voice is commonly regarded as having a bandwidth of 4kHz. Assuming 8-bit ADCs are used, the RAM can only last about one second. Furthermore, although my knowledge with speech processing is limited (I do know basic DSP though), I would associate it more with transforms, correlators and markov processes, which need even more RAM.