Do Turntables sound better with time?

NO.  Maybe the cartridge, but in my experience (55 years since my 1st turntable) a turntable will not change, unless it starts to breakdown. As noted above, other factors may improve the sound.

Any audible difference would be minimal but we have ta accept the fact that for a new set up many things would change with use. Bearing, motor, power supply, tonearm cabling, let alone cartridge. Can we isolate any change individually?

I’m sure it’s possible that the bearings in the motor can do some form of “break in” as well as the suspension ( if it has some). Certainly, the cartridge, just like a speaker but in reverse, which converts mechanical energy into electrical may need some break in. 
 

There are those who think wires & cables break in too & although probably not measurable, might be true. I think this also be a matter of our own internal “wiring” meaning our brain & nervous system getting used to new & different sound.

@lewm 1+, There are many reasons the sound of a system can seem to change from barometric pressure and humidity to the mood of the individual at the time. In most cases I do not believe components "Break In." Transducers might but not electronics, turntables or tonearms. I think it is our heads that break In. We accommodate to the sound of a system over time and I have seen people accommodate to systems that were severely out of whack. We tend to like what we are use to listening to. People honestly think a component sounds better and it does to them. It is easy to see why people think items "break in."  They are just blaming it on the wrong component.