I need to leave Tails on for a couple of hours in order to download a bunch of files. Does the screensaver in any way interfere with Tor? Will it reduce my anonymity and/or cause the downloads to fail?

I need to leave Tails on for a couple of hours in order to download a bunch of files. Does the screensaver in any way interfere with Tor? Will it reduce my anonymity and/or cause the downloads to fail?