Is this PIC micro-controller powerful enough to drive PWM LEDs?
Looking at the datasheet for that device, you would need to use the output compare function to control the PWM.  However it looks like you wont be able to set 16 individual PWM periods, therefor this may not do what you are hoping.  You would probably be better off using the outputs pins as general I/O and using interrupts to create your own PWM periods.  If you do it yourself using interrupts, your choice of micros may open up.