Yes, it’s possible.
The Game Logs System (GLS) plugin is compiled for all configuration modes and activates at runtime based on the settings. To enable the plugin in the shipping configuration, go to Project Settings → Plugins → Game Logs System → Enable Logs In Shipping builds in the editor.
To ensure that GLS captures logs in a distribution build, use GLS_LOG instead of UE_LOG. Unreal completely removes UE_LOG calls in shipping builds, so GLS needs to intercept logs differently.
In a shipping build, you can open the GLS overlay panel by holding two fingers on the screen of the mobile device during gameplay. This will display the logs in a tab on-screen, where you can filter them by specific categories as needed.
Additionally, make sure to set the following in your DefaultGame.ini file:
[/Script/GLS.GLSSettings]
bEnableLogsInShippingBuilds=True
These settings need to be applied when packaging the build.