Nope. GenieGo only downloads to supported smart phones, tablets and PCs.
But note that the GenieGo "download" process involves two steps. The first step, "transcoding", does not require the PC to be on after you select the show(s) to download. That step prepares the show inside the GenieGo's memory for future downloading to your PC, smart phone or tablet. That process takes about as long as the show is, so a 1-hr show takes about 1-hr to transcode. Only one show transcodes at a time. Once the shows are transcoded, then they can be downloaded to your PC much faster. On my home network, a 1-hr show only takes a few minutes to download. And, for the actual download, your PC is on.