Does a turntable make a DRAMATIC difference?

RV, something to consider that I've failed to mention. I don't know if my experience is unique or if it is something that other attentive audiophiles have had to deal with. Back in the day when vinyl was my primary source of music I had a fairly good (near SOTA) system but not a particularly fine, and comprehensive, collection of music.

I finally started to pay attention to digital in the 90's and concurrently started ignoring vinyl. All the new (to me perhaps), unexplored, music was coming out on CD's so I followed it. I tuned my system to get digital listenable and I succeeded (I think) but, interestingly the changes I introduced seem to degrade my vinyl system's reproduction (not that much perhaps) so it was easy to continue to ignore my records and just play CD's.  Being unable to get both sources on equal footing I simply gave my analog system (and records) to my grandson-in-law and moved on with just fond memories of the greatness of vinyl.  He's happy and so am I. And, ultimately, digital is so plug and play as opposed to the set up AND maintenance of a vinyl system so I have more time and less to worry about.

ghprentice, I suspect I might, just might mind you, be much more anal than you when it comes to vinyl. :-)

Look for a great vintage manual table that was issued with a great tonearm and see if you note a difference. If you buy a good one and there is no difference you will always be able to sell it for the same amount or possibly more. The JVC QL7 would be an example of such a table. I’m guessing $400-600 would get you a good one. There are others but you will pay more for other more highly recognized makers and not have much if any significant benefit.

I upgraded table and arm in a controlled circumstance-- same room, system and phono cartridge. The difference with the better table/arm set up-- fewer sonic artifacts from the better table/arm combo. 
Sometimes, it is hard to discern an artifact until it is gone. 

For example, the "halo" of sound that I often associated with record play is simply absent on the bigger, high mass table and linear arm--

The bass is better too, but to fully appreciate that,

I needed to augment the bass reproducing capabilities of my system-- 

Now in a bigger room, with additional subwoofers.

And the thing that really made a difference was a change of cartridge-- not so much fancier or more expensive, just different voicing. If I had made that cartridge change with a different table/arm and without the bigger room/augmented subwoofers, would it have been as dramatic? I doubt it--but it took more than just a change of cartridge or table to get to this point. The improvements were cumulative. Is that true in every system/circumstance?

I don't know. 

@OP. It depends on how good your digital is. Back in the 80s when CD appeared a Rega 3 would obliterate the players that are available.

That's not the case any longer. Small volume mechanical engineering costs lots of money so, arguably, its become more expensive to make system improvements in the analogue domain than in digital.

My reintroduction to vinyl was a rega p3 and dynavector 10x3 cartridge.  The synergy with the tonearm was the key.  Had the opportunity to buy a higher level dynavector cart that someone brought back a few months after purchase to upgrade.   Sounded awful and went back to 10x3. The rega tonearm was a great value in its price range but not up to demanding cartridges