This stuff was usually easily adjustable, so you could compensate for various irregularities. But some turntables had built-in strobe lights for aiding in adjustments, so if the line frequency was off then the strobe would be off and then your adjustments would be off, too. And even if generally well-adjusted, should the line frequency vary too much while playing a record then you would probably notice that. During musical passages it would probably definitely be noticeable, while during singing and speech maybe not at all.

Most audiophile gear from back in the day used DC motors or AC motors with multiple phases driven from on-board oscillators and advertised that fact. Consumer stuff tended to use synchronous motors. But even relatively high end stuff (Thorens TD 160 for instance) would use net-synchronous motors.

Vintage gear has interesting challenges, such as finding good drive belts, they tend to turn to sticky mush after a couple of decades.

Depend on how vintage the gear is. After '70's when quartz crystals became the norm for everything involving hertz? No need to worry. Before that? Yeah, pretty much