Will a $700 turntable outperform a CD player?

Maybe,

But in the long run, do you want to pay for the maintenance of a turntable.
Turntables are great from the retailers point-of-view. Because they wear out. Which means they have a new customer and additional cash flow over time from this sale.
New belts, new cartridges, bearings replaced in the tonearms, possible motor issues and then the suspensions and occasional tuning to make sure it is up to specs. Plus, all the accessories to upgrade and maintain your TT and record collection. (More so with belt drive TT than direct drive TT)

If your buying a TT, make sure it is new and not used. A used TT is like buying a 20 year old BMW and thinking it will perform just like a new car. 

When a Paul McGowan of PS audio states that DSD audio sounds better than vinyl, I think you can see where the future of audio is going.

Finding LP's at great prices is fun, that's why I still have my TT and to listen to my collection of Lp's. With the prices of used CD's declining, maybe the bargains will be this format for awhile. 

The easiest way for you to resolve this issue is to A-B the same recording on a turntable and in a CD player. I did this years ago, not only for myself but for many friends and family members.   Everyone was amazed as to how much better vinyl sounded than CD.  The 
CD sounded as though it was muffled compared to the vinyl. I urge you to conduct this simple but revealing test. 

No DJ table, or direct drive table will match an “audiophile”turntable designed in the post mass market vinyl era. I would consider the Clearaudio Concept the most affordable destination turntable. The closest thing to a Concept under $1k, would be a Project X1.
This will sound more natural than digital in some ways. Pretty much anyone can hear the difference and is drawn to vinyl IF they are not focused on low level noise, pops, etc.
The above turntables are quieter than you would expect.
i get to listen to the best DAC in the world - the DCS Vivaldi, anytime I want at work. Even that can’t quite match a good vinyl rig for naturalness - your brain misses the 80% of timing info that digital throws away.

If it has the right phono stage!

To OP, 

There are many variables involved.  If you have a well mastered CD and compare it to a poorly mastered LP or the LP is very noisy, then CD can be way better sounding.  Vice-versa too.  

It really depends on your determination to source and procure well mastered versions of albums on LP.  Things like where and who pressed the records also comes into play.  You might get frustrated being a few new records only to find that they are damaged right out of the package and need to return and get replacements.  Or maybe you want to seek out the very best pressing or mastering of a particular favorite.  If this is your cup of tee, then you might want to get into the vinyl game. 

If so, I'd recommend getting something like a Project Debut Carbon turntable with an Ortofon 2M Red cartridge pre-installed for you.  From a reputable dealer that will accept returns.  This way you might find that it is not for you and you can either return or sell.  Either way, your initial investment is not that high...I think $500 or less.  Especially if you already have a phono input in your receiver or amp to try.  If not, you will also need to get an external phono-pre-amp (aka phonostage).  

Otherwise, you have a good DAC and I think it might be better to explore getting a streamer.  The Bluesound Node 2i is a great product for not a lot of money and can introduce you to the world of music streaming services such as Tidal and Qobuz.  This is the best way to explore new music!

It also depends on what you listen to.  If most of the music you like is newer and mastered on digital, then I think there is little benefit to getting a analogue vinyl front-end.  I find that albums recorded in the analogue domain such as Blue Note albums from the 50's and 60's and remastered by Kevin Gray and pressed by RTI sound magical!  Much better than any digital files or CD.  However, Whitesnake (1987) sounds just as good (or bad LOL) on the CD as the LP.

Lastly, generally speaking a well mastered and pressed LP can be more enjoyable to listen to for most people.  After all we hear in analogue.  My experience is that a decent $400-500 turntable can sound great.