Signing out of the YouTube app on Android will sign your account out from all Google apps on the device (like Maps and Gmail). You could try browsing on the YouTube app privately using Incognito mode. Hope this helps.
First off, no it won't I did this so many times on my phone and never was signed out from all my apps and using Incognito will not log you back in and YouTube email login is too secured to even log back in without being forced to use two step verification even though, same device