No. The communication goes from the remote to the TV, and the TV sends it on to the Sonos. If the TV is not on, it won’t pass any information on to the Sonos. 

I thought that might be the case. Shame there’s no learn function using IR.

There’s an entire FAQ on how to turn on IR for the LG Magic remote, and how to set up the commands in the controller for a PLAYBAR, which would also work with the Arc. However, it will only control the room the Arc is in, and none of the grouped rooms. 

However, I’m under the impression that the TV set sends a ‘power down to a limited set of functions’ when the TV is ‘off’’.  You’d need to double check with LG to ensure that all IR is active when the TV is off. 

Another thing to be aware of. Sometimes, when the TV updates itself, it turns off the IR on the remote, and you have to set it back up again.