Convolutional coding can be implemented on any general purpose microcontroller.
Thus the simple answer to your question would be yes. Considering "performace": depends on your needs. There might be alternatives with more output per mW if this is an issue.
The best thing would be to have a look at the benchmarks for complex FFT calculation.
While real DSP`s are specialized for those operations, they have high throughput at lower processor speed. E.g. DSP 56321 (Motorola/Freescale/NXP) needs 8201 cycles for one Radix-2 DIT calculation (assembler) with 1024 points. At 275MHz he needs 30µs for that job.
A Cortex A15 at 1GHz needs 43,92µs (http://preview.tinyurl.com/y7csu3s3).
A Cortex A9 with NEON SIMD engine 170µs (see conclusion at http://preview.tinyurl.com/y78927a4) or 75µs (FFTW see https://bitbucket.org/jpommier/pffft )
Sometimes it is very difficult to get values for absolute calculation times.