Nope.
Mono button sums left and right channels of a stereo recording together. Mono recordings are already summed together so no effect from the button.
Mono CDs are stereo with equal tracks left and right, and no noise, so no effect on CDs. But all vinyl has "stereo" noise so if you play a mono record with a stereo cartridge you will hear the music as mono but the noise is stereo, so mono button can sum the noise to the center to be less distracting. A mono cart playing a mono record should be no diff with mono button.
On modern recordings of popular genres bass is usually panned to the middle, so mono mode will mostly effect the wider panned mid/treble. But classical symphonies and some 60's early stereo music can have more separation in the bass that can sound muddy when summed to center. ymmv