Is it possible to have vinyl nearly noise free?

I can’t imagine buying LP’s used and not having a serious record cleaner. I "deep clean" mine only once (before their first playing), just dusting after that. I started with a Watts Preener (if you recognize the name, you too are old), and was very happy when the original Discwasher was introduced; much better! The Keith Monks was the first serious cleaner (nozzle and thread design), but it cost a fortune. The introduction of the VPI and Nitty Gritty vacuum machines was a Godsend---finally, serious record cleaning at a workingman’s price! I got a Nitty Gritty first (no pun intended ;-), but found it lacking in some ways. Next was of course the VPI, which I found much more to my liking. Now there is ultrasonic, which has it’s own advantages. At their prices, there is no reason a record collector can’t have both! And a dusting brush or two; I have a Decca, an Audioquest, and a Hunt.

 Cartridge certainly makes a difference. I had a shelter 7000 that was amazingly quiet. 

I tend to agree with atmashpere on this without even paying attention to the engineering jargon.  I've heard enough different variations of carts/tonearms/phono stages to hear the difference in how some combos play quieter than others.  My RCM also sits unused most of the time.

I don't think cleaning is a waste of time, but I'm sorry, a ten step cleaning process or cleaning each side before playing takes all the joy out of it for me.  

Like others have said, get a good pressing, get a hardware combo that plays quietly, get a brush for removing dust, play, and enjoy.  The better vinyl setups will push the music forward and the noise to the background.

Certainly, yes, but I would recommend changing your process.
First-order considerations:If the vinyl is already damaged by dirt that's been pressed into the vinyl, then I know of nothing that can be done.  But let's assume that you start with a dirty but undamaged LP.  Some LPs come from the pressing plant with damage, and you can't do much about that.  But if it's been pressed in a high quality environment (for example, new pressings sold by Acoustic Sounds) it should be good.  The best, quietest pressings I have ever heard are made by Music Matters Jazz using a vinyl formula they call SRX.
Even new LPs must be cleaned before the first playing, to remove surface impurities like "mold release compound" that prevents the LP from sticking to the stamper.

First use a wet vacuum wash, such as a VPI Typhoon.  This removes large particles.  I do this only once when acquiring an LP, whether new or used.  There are lots of opinions about the makeup of the liquid used to wet down the LP, but I'm not an expert on that.  I use l'Art du Son concentrate mixed with distilled water.

Second, run it through an ultrasonic cleaner.  That removes very tiny particles embedded deep in the grooves.  I use a KLaudio and do it before each listening.  The KLaudio machine is fully hands-off wash and dry, so it isn't a bother.  Go make a cup of tea while it runs for 5-7 minutes and both sides will be clean.
The results amaze people regularly around here, who think I'm playing digital.

Second-order considerations:As others have said, your cartridge / needle geometry makes a difference.  Generally, the better ones are less affected.
If you buy used vinyl, watch out for crumbling foam inserts.  Box sets, especially classical box sets, used to have thin 12 x 12" foam sheets inside as cushions.  Over time the foam disintegrates into powder and gets everywhere.  It then seems to bond chemically to the vinyl surface and becomes impossible to remove completely.  If someone ships you a LP set like that, refuse and return it.

The better vinyl setups will push the music forward and the noise to the background.

I think that....

Music Lovers push the music forward and the noise to the background.

Audiophiles will hear every little tick and pop. This is also one of the reasons that those that never had history with vinyl - prior to CD - struggle with vinyl.     

Vinyl has a noise floor.

How quiet it is will depend on who did the cut on the master disk.

It varies from record to record.