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Depends how bad the quality is. It's like all engineering, £50 car that can drive from A->B is doing it's job, you get there. £50k car should be a nicer experience.
I've got fussy because I have lots of mint records that are clean and I don't get much surface noise so it can bother me if it's there. On the other hand, 45's that come from my Grans collection that have been played by my parents and aunts on a little setup with a dodgy needle are noisy but still nice to listen to.
I wouldn't play a £200 pressing with a crappy needle, it just doesn't make sense. I have played plenty of crappy records with a decent needle though.
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Does the quality of the record make much difference with a poor quality needle and set up?
Define poor quality?
I can tell the difference between a good and a bad mastering or pressing with my modest set up (40 year old Rega Planar 2 with original Ortofon cart/third party stylus, Arcam Alpha 3 amp, Celestion 5 speakers). Probably about £350 all in with today's ebay prices. You don't need to spend thousands to get a set up where the recording is the limiting factor.
Does the quality of the record make much difference with a poor quality needle and set up?