If you have a line conditioner, does noise matter?

Two different animals.
The voltage stability concern is a voltage regulator
The noise in the A/C line is a power conditioner.
A few products do both.
When a person speaks about a 'Power conditioner' they are referring to the noise in the line attenuator product, pretty much exclusively.
I cna say most anywhere in the USA folks do not need a voltage regulator. The usual voltage swings in a residential line do not merit bothering with. And for folks who do have problems, it is usually due to faulty equipment outside on your A/C grid. (IE complaining like hell to the utility provider should get it fixed.)
For powerline grunge, the power conditioner is the way to go.
They come in all sorts of flavors. Choose your poison.
est idea is start with a cheaper one, and see if it does ANYTHING you like, with some experiene one can find a power conditioner that does what you want, and not do what you don't like.
I started with ferrite claps, then Adcom, Monster cable, now A big Furman REF20i.

While is doesn't adjust line voltage, a sub category of power conditioner includes an Isolation Transformer.
My PanaMax has all the usual power conditioner claims but also has a 400va iso trans. Into this, goes all my low power and digital equipment.
If I could have found the Furman Elizabeth refs, I may have gone that way. As it turned out, the Panamax was available. Not inexpensive, either.

Many, if not most, amps DO NOT like power conditioners. My experience has been mixed. My Rotel RB-1070 really hated the conditioner. My ancient Carver cube? Seemed good with it.
My PSAudio ICE integrated likes it too, but has its own circuit and Solosist outlet.

When it comes to noise reduction , Shunyada is king .

Next to power regeneration, IMO balanced power is the best bet. The technology is proven to significantly reduce power line noise. I've been using balanced power for the past 6 1/2 years. Unless there are wide fluctuations outside normal voltage range and/or brownouts, IMO voltage regulation is not needed.

I have a PS Audio Power Plant Premier, a DIY parallel AC filter, RC filters inside my preamp and EQ, snubber caps on all tube heaters, ferrites on the heater and B+ lines, and my preamp uses DC for the signal tube heaters. Every single additional noise reduction step decreased background noise and improved the sound, and I started with the PPP as the first one! They are additive.