The answer to the OP's question is actually "yes". A digital connection from the tv to an input on the receiver will enable you to feed audio from the PC through the TV to the AVR.
However, the output will likely be stereo as most TVs will not pass through encoded multichannel sound. So, running HDMI from the PC to the receiver is likely the better way to go. Of course, you'll need to add an HDMI connection from the receiver to the TV for video.
None of this has anything to do with your existing STB set-up.