You can put the amp into standby, or you can mute the amp, or put it into standby or you can select a different input than the CD player before turning the CD player off. The point is that the CD player MAY emit a pulse when it is turned off which you would not want to amplify and feed to your speakers.
Most tube CD player outputs simply use the tube as a buffer. These small signal tubes would probably last LONGER if you don't turn the CD player off. Turning on a tube results in a quick inrush of current that rapidly heats the tube causing stress. This is what causes most of the damage to a tube. I would leave the CD player on all of the time. Also, when you turn the CD player off, the capacitors in the player discharge. It can take a lot of time for the caps to fully charge up and for the player to sound its best.
Most tube CD player outputs simply use the tube as a buffer. These small signal tubes would probably last LONGER if you don't turn the CD player off. Turning on a tube results in a quick inrush of current that rapidly heats the tube causing stress. This is what causes most of the damage to a tube. I would leave the CD player on all of the time. Also, when you turn the CD player off, the capacitors in the player discharge. It can take a lot of time for the caps to fully charge up and for the player to sound its best.