Unfortunately, yes (or better no). It depends only on Avast being installed or not. Avast being turned off, taken your question litterally, does not matter. Currently, Windows Live works and AVast is not installed (uninstalled).

Proof is a big word, but evidence is present. I even double-checked, this means: first I was hit by the problem. Then I deinstalled Avast and activated Windows Defender. Two weeks later I installed Avast again (Real-time part of Defender already turned off, and it deactivated itself completely by presence of AVast). Then I deinstalled Avast and installed another virus protection.

Edited for misspelling and non-native english.