Of course they would. As far as they are concerned you never owned
anything but plastic.

Home recording is legal. Since there's no digital restrictions on CDs and LPs,
even the DMCA can't stop you. The MAFIAA would tell you that downloading is
illegal and "stealing" but they dare not face a court with that line. The simple
reality is you are at home, recording (making a copy) with your computer, but
you are getting it from the internet instead of a CD in a drive or a turntable
plugged into the sound card.

The law comes in only if someone uploads music from your computer on the internet.
Even then, it is strictly a civil matter and they would have to sue or
leave you alone.