Will an IC that requires an Oscillator work without one?
I'm confused. I just looked at the PL2303HX datasheet (http://www.adafruit.com/datasheets/PL2303HX.pdf) and I see no sign that a crystal is required, or that it is even possible to use one! AFAICT, the clock generator is internal to the chip.

I'd say that your problem lies elsewhere.