The same people using special rectifier tubes because they sound better, are some of the same folks that swear by having a SHIELDED power cord.
To the original question re: sound quality, sure if the tube is weak, it may not be supplying enough current to the filter caps so your voltages are all low.
I guess another way is if the 5U4 is shorting and sparking internally, yep, it won't sound good at all. A bit crackly!