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.