timppu: I presume yes, at least for me the GOG Downloader works great from my work internet (corporate) connection, which is behind a proxy. I don't even have to put proxy settings anywhere in the downloader, it just works.
FangLargo: Huh. Curious. Mine just didn't like working. The indicator on the bottom left stays "Offline".
Are there certain ports that need to be open?
Downloader uses port 80, everything goes through normal HTTP requests. A firewall or antivirus software may also be blocking the Downloader, please verify that's not the case. Let me know what you have come up with. Thanks.