Dimmer switch on the same electrical line

With my solid state- yes.

Depends on the dimmer and it depends on the quality of the power supply in the amp. Many of the cheaper dimmers will cause DC offset voltage back out on the AC line. This DC offset will cause a toroidal power transformer to buzz louder than normal.

Also many of the cheaper dimmers will put odd harmonics back out on the AC power line.

I have a RFI problem which causes distortion in my system. After trying everything to find the source of the distortion, I was told by a member to try using a circuit with no dimmer switch. So I did with no difference in the distortion levels. At least for me it did not make any difference.

I have a dimmer switch in use with florescent lamps and I have no problem and it is on the same line my tube amp is. A florescent dimmer is a special type so it may not be a match to your situation.

According To Robert Harley it does.