Can a refractometer be used for testing final gravity?

Perhaps, but I have tried this with a couple of online calculators and with brewtarget and each time, the calculated final gravity is significantly lower than my actual hydrometer reading. I finally gave up. I actually find the hydrometer a bit simpler for final gravity anyway. The refractometer with ATC comes in handy with hot first and second runnings and pre and post boil gravity. I can also use it without wrecking my plastic at high temps. Final gravity is always room temp (or lager temp) and I like to taste my sample at that point as well.

As far as I know, you can determine the final gravity solely with a refractometer only if you know the original gravity (either with a hydrometer or the refractometer). I am a small-batch brewer, and exclusively use a refractometer for gravity measurements. A few tips:

1. You have to calibrate your refractometer to read zero when using distilled water as your test sample.
2. If your refractometer has a specific gravity scale (e.g., 1.050), don't use it. Many refractometers have an incorrect scale because they have used a formula for the cubic equation to convert from degrees Brix to specific gravity that was incorrectly published on byo.com. Take the Brix reading and use a calculator to convert it instead. Source 1; Source 2. Here is the incorrect byo.com online article.
3. The refractometer is designed to read samples of sugar water and fruit juice, not wort. You can determine your refractometer's wort correction factor. To do so, you need to take concurrent hydrometer readings. The wort correction factor is usually around 4%. I decided that it is impractical to take hydrometer readings when brewing small batches, and that I will just assume that adjusting by 4% is close enough for my purposes.
4. This calculator by Sean Terrill is probably the most accurate to determine final gravity.

Yes, but you have to factor in the alcohol so you'll need a refractometer adjustment calculator. Northern Brewer has one on their website and there are other online calculators as well. But no two calculators seem to agree perfectly.

Personally, if I'm in the ballpark I'm happy. But if you want to be certain of getting the most accurate measurement possible you could do a side-by-side comparison of hydrometer measurements vs adjusted refractometer measurements using various calculators to see which comes closest. Then just use that going forward.