They only way I can think of is through a 3.5mm splitter. You would run the analog out of your soundcard to the splitter, then connect your Logitech 3.5mm cable to the splitter, and use a 3.5mm cable from the A50 base station to the splitter. Plug the USB cable of the Astro A50 base station to the PC for power, but on your audio output, assign the analog audio out as your primary.
This will not sound as good as using the USB DAC or the optical input, but it will work.
This will not sound as good as using the USB DAC or the optical input, but it will work.