Does remote control degrade the sound of tube preamps?

Yes, $600 to $1,000 IS a lot to spend on a volume control component.  But, it is one of the most important piece in the signal chain and can seriously degrade the signal and/or cause channel imbalances if the left and right channels do not track perfectly.  Spending for quality here makes far more sense than spending it on other stuff, like fuses, and fancy power supply caps.  

Yes there are MANY ways to employ both manual and remote volume control.  One of the most interesting is the EMIA approach of using an auto-former with many discrete taps that are relay switched.  I believe there are other transformer-based volume controllers, some even utilizing remote switching.  This probably represents the most complex way of doing volume control.

I also like the approach of having only one fixed resistor in the signal path, with volume determined by relay switched set of resistors shunting part of the signal to ground.  

There is nothing that makes remote controlled volume control inferior in sound quality.  If it is implemented with a motorized potentiometer, the quality is entirely dependent on the quality of the potentiometer, not on the motor whose only job is to twist the shaft just as your hand would also do.  Even if your volume control is a rotary step attenuator, it is possible to physically move the dial under motor control (Ayre does this).  Many very good attenuators are ladder step attenuators that are switched by relays, and the relays are always remote controllable.

It is so important to get volume set just right to get optimum sound quality and satisfaction, and that can only be done practically by remote control as you sit in the sweet spot and instantaneously hear the result.  Remote control of volume is pretty much an essential feature, not merely a convenience.  Without it, one tends to just live with something close to the right volume instead of actually determining what is the right volume.

To be clear, adding remote control functionality to volume control does not degrade sound, but, if providing that feature means cost cutting on some other aspect of product, that could hurt the sound quality.  If providing remote volume control means going with an inferior potentiometer that has a motor built into it, instead of a superior manual potentiometer, that would hurt the sound.  I have a $1,000 Alps RK 50 manual potentiometer in my headphone amp.  If a builder wants a motorized version, the builder would have to engineer this and modify the potentiometer at considerable cost to so do.  That means it is "possible" to get that level of quality, but it might not be that practical.