No, of course not... whichever device is being used for output not a device that's turned off.
As for more storage... don't know, how much hard drive space do you have left. 20gb, 40gb, 60+gb?
Logic should normally be the only program running as it uses a huge chunk computer resources.
How much RAM does your computer have.
Here's the point, no matter what, Logic should not make unexpected audio output in the decibel range, it's something that should not happen in professional software.
That said it doesn't happen to everyone but from past postings it's not a stranger to many users.