Upgrading to a stand alone DAC

Would I hear a significant difference at this price point?

Difference in DACs can be huge or very subtle, depending on how resolving the rest of your system (and room) is. 

Chord Qutest is an amazing DAC. Get one used around $1,000 and flip it if you don’t like it. I owned it and several DACs later still hold it in high regard. 
Another good choice is a used Benchmark DAC 3 - slightly more detailed than the Qutest but more analytical/sterile sounding. PS Audio DSD DAC is excellent as well. You can score one in your price range. Smoother more analog sounding but very musical with excellent detail retrieval. 
Stick with a major brand DAC and you should be fine  

Good luck in your search. 

Would I hear a significant difference at this price point?

Aged and untrained ears are not going to hear significant differences.

But, the slightest difference can become quite significant for someone over time and dominate their psyche (most audiophiles might fall in that category).

If your budget is restricted to 1500, the Gustard R26 (the R2R version) is an incredible dac that often goes on sale for right under 1500 dollars...You could rip all your CDs, put them on a NAS and it will stream those files from your NAS, without the need for some extra streamer and cable botching things. Most stand alone dacs won’t offer you that capability..... Err...awful name though i know (rhymes with some bastard munching on custard), but if you can get past the brand name, it’s a good dac.

I'm a Gustard guy. I own two X26 pro and waiting for a new A26. From the reviews you will get more clarity with the A26 than the R26 but with none of the digital brightness of the X26 PRO, which is already at a minimum. The A26 sounds like the best of both world and I can't wait to get my hands on it Wednesday. The R26 would definitely be too dark sounding in my house of stereo, gone the r2r route before but not for very long. It's all room and system dependent.

@baylinor

My Gustard R26 is anything but dark. Not all lacking in detail or clarity. Not in my setup, anyway. 

@sls883

I have major amount of absorbers and bass traps in my house of stereo, plus fully carpeted, meaning I prefer Uber detailed equipment. Like no tubes. Been there, done that. Plenty of diffusing too, but the room construction does not react well to r2r. Glad it works for you.