It depends.
As long as you have good enough nutrient export (and you're careful not to overfeed/have too much of a bioload relative to your export/use RO-DI water), your tank should be fine. If it isn't (nuisance algae, etc), then you need to increase export in some fashion. I don't consider partial water changes to be a good means of nutrient export, partially due to the math (if your nitrates are at 20, a 10% water change reduces them to 18. That's a pretty minimal drop, considering that whatever is driving your nitrates up will continue to add nitrates at the same rate) and partially due to the effort for that reduction. I do think that they are useful, just not for nitrate/phosphate/organics reduction when there are more effective methods that are easier (and cheaper in the long run).
A good skimmer will remove 20-30% of dissolved organics (35% on the high end for really expensive high performance skimmers) per Advanced Aquarist (
https://www.advancedaquarist.com/2010/1/aafeature); interestingly, skimmer design didn't really matter much as "bubbles are bubbles" for efficiency. They also have articles on what is present in actual skimmate (mostly inorganic ions, with a minority being actual organics -
https://www.advancedaquarist.com/2010/2/aafeature). Skimmers do oxygenate the water and help with gas exchange. If you do get a skimmer, it will certainly help with nutrient export to a point. I wouldn't spend a lot of money on a skimmer for efficiency reasons; the money is for reliability/build quality/ease of disassembly/etc.
Refugia/algae reactors/algae scrubbers and carbon/GFO are other good means of nutrient export. SBReefs had a $75ish grow LED bulb with a clip-on mount that looked like a good value. The more you have of these, the less important skimming becomes. Also, before I forget, a twice weekly rinsed filter sock removes nitrate and phosphate from excess food/organic materal before it breaks down.
I personally run a skimmerless 32 gallon tank; with a good refugium light ($25 LED grow bulb and a gooseneck clip-on mount) and some Chaeto (along with live rock and a 1" sandbed), I have nearly undetectable levels of nitrate and phosphate. It's not ULNS by any means, but it's very simple and works very well in my experience. I have thought about adding a skimmer (a small Tunze, as I have a 9001 and a 9004), but with the exception of a Valonia outbreak I'm not sure what good it would do above the refugium. I tried a bit of vinegar/carbon dosing, but there was some sandbed cyano that has been gone for some time (that may have been sandbed debris, so that's not clear to me).
Soo . . . it depends. With good nutrient export by other means, you may be able to get away without a skimmer.
Hope this helps!
