If the tuner is taken off before performing then it has to be put away or else risk getting lost or broken. This adds an inevitable delay before the performance begins. The guitar could easily get knocked in the process and end up out of tune again.

No! Leave the tuner safely where it is and put it safely away when the song is finished. If you don't like it, don't look. Concentrate on the finger work or the singer's face instead of fussing about things that aren't important.

DC