The short answer is no.
Now, for the long answer. Many people on the internet will proclaim that there is no difference between many of the lower-cost ARs (or AR parts) and the more premium ones. Basically, they argue that people who are over-paying are just not that intelligent. You see, a forged Anderson Manufacturing receiver is forged at the same place many other receivers from other manufacturers are. Palmetto State Armory sources pretty much all their parts from mil-spec manufacturers - companies that are known to produce military specification quality and quality testing. Aero Precision forged receivers are remarkably similar to Spike's Tactical receivers - indeed, they are similar to ALL mil-spec manufacturers. Places like Anchor Harvey are actually doing the forging for these companies, from Noveske to Anderson. There aren't that many forges in the US that produce these receivers and pretty much anyone who isn't CNC Machining their own receiver is getting their forged receivers from the same place, essentially. This idea that they are all the same is true, to a point.
There is a difference between buying, say, an Anderson receiver vs a Wilson Combat receiver. Anderson seems to generally produce good parts that are within standard military tolerances (.001"), but Wilson Combat guarantees +/- .0005" tolerance at the key points of contact on the receiver. That makes for less play in the gun, which effects all kinds of things - accuracy on follow up shots, ensuring proper fit of parts, ensuring proper function of parts, etc. However, Anderson receivers will typically function properly and fit well enough for virtually all practical purposes. The other key difference is the quality control. Do you want to try to build your gun, but find out afterward that you have parts not fitting right, especially when that is causing malfunctions? Anderson will make it right if on the rare occasion it's not right the first time, I'm sure, but that still leaves you without a working rifle and with lost time spent finding a part is out of spec. It sounds like I'm picking on Anderson - I want to be clear, I am not - but, they sell their parts very cheaply and there is a reason why they can do that and stay in business. (Hint: it's not just that other companies are greedy.) The point here is that there can be differences, mostly in the fit and finish of the parts, when buying from high-end manufacturers vs low-cost manufacturers. Quality control is what makes sure it's right the first time and that is what the high-end manufacturers are charging for, but it will be rare for any of these major companies to produce a "bad" product. So, if you want tight-fitting receivers with no rattle, precision tuned trigger springs, or hyper-accurate rifling in your barrel, you would be wise to pay a little more to get premium parts to ensure that they are put through more rigorous quality control processes and made to more exacting tolerances. It's also worth noting that some manufacturers produce parts with better materials or better processes, such as Cold Hammer Forging barrels or special coatings on BCGs. These things can significantly improve performance, durability, and reliability. This should not be overlooked when selecting a rifle or parts for the rifle. It's a cost/benefit ratio that you have to figure out for yourself.
If you only need to hit a man-sized target at 200 yards and want to make a reliable, if not competition-level accuracy, rifle, then you need not worry. Go ahead and buy from any major manufacturer and test it to ensure it's cycling properly and isn't wearing prematurely. If you do, the vast majority of the time, you will find that the gun or parts will function well, no matter who you buy from. The manufacturing technology has become so good that we don't have to worry much about tolerances in today's AR market. However, I want to stress that you need to verify things are built properly by testing them and visually inspecting them because any manufacturer can produce a lemon. If you are doing that, you'll be able to build a good, reliable rifle for a very reasonable price.
So, do you NEED an expensive AR? If you just need to meet the criteria I mentioned above, ie being able to hit a man-sized target at 200 yards, then the answer is no. There are reasons you might want or need to pay more, such as extreme accuracy, but you must answer the question of if you actually need that. For most people, for most practical reasons, the answer is no.