EDIT:
From your update, you may misunderstand what the NEON processor does. It is an SIMD (Single Instruction, Multiple Data) vector processor. That means that it is very good at performing an instruction (say "multiply by 4") to several pieces of data at the same time. It also loves to do things like "add all these numbers together" or "add each element of these two lists of numbers to create a third list of numbers." So if you problem looks like those things the NEON processor is going to be huge help.
To get that benefit, you must put your data in very specific formats so that the vector processor can load multiple data simultaneously, process it in parallel, and then write it back out simultaneously. You need to organize things such that the math avoids most conditionals (because looking at the results too soon means a roundtrip to the NEON). Vector programming is a different way of thinking about your program. It's all about pipeline management.
Now, for many very common kinds of problems, the compiler automatically can work all of this out. But it's still about working with numbers, and numbers in particular formats. For example, you almost always need to get all of your numbers into a contiguous block in memory. If you're dealing with fields inside of structs and classes, the NEON can't really help you. It's not a general-purpose "do stuff in parallel" engine. It's an SIMD processor for doing parallel math.
For very high-performance systems, data format is everything. You don't take arbitrary data formats (structs, classes, etc.) and try to make them fast. You figure out the data format that will let you do the most parallel work, and you write your code around that. You make your data contiguous. You avoid memory allocation at all costs. But this isn't really something a simple StackOverflow question can address. High-performance programming is a whole skill set and a different way of thinking about things. It isn't something you get by finding the right compiler flag. As you've found, the defaults are pretty good already.
The real question you should be asking is whether you could reorganize your data so that you can use more of OpenCV. OpenCV already has lots of optimized parallel operations that will almost certainly make good use of the NEON. As much as possible, you want to keep your data in the format that OpenCV works in. That's likely where you're going to get your biggest improvements.
My experience is that it is certainly possible to hand-write NEON assembly that will beat clang and gcc (at least from a couple of years ago, though the compiler certainly continues to improve). Having excellent ARM optimization is not the same as NEON optimization. As @Mats notes, the compiler will generally do an excellent job at obvious cases, but does not always handle every case ideally, and it is certainly possible for even a lightly skilled developer to sometimes beat it, sometimes dramatically. (@wallyk is also correct that hand-tuning assembly is best saved for last; but it can still be very powerful.)
That said, given your statement "Assembly, for which I have absolutely no background, and can't possibly afford to learn at this point," then no, you should not even bother. Without first at least understanding the basics (and a few non-basics) of assembly (and specifically vectorized NEON assembly), there is no point in second-guessing the compiler. Step one of beating the compiler is knowing the target.
If you are willing to learn the target, my favorite introduction is Whirlwind Tour of ARM Assembly. That, plus some other references (below), were enough to let me beat the compiler by 2-3x in my particular problems. On the other hand, they were insufficient enough that when I showed my code to an experienced NEON developer, he looked at it for about three seconds and said "you have a halt right there." Really good assembly is hard, but half-decent assembly can still be better than optimized C++. (Again, every year this gets less true as the compiler writers get better, but it can still be true.)
One side note, my experience with NEON intrinsics is that they are seldom worth the trouble. If you're going to beat the compiler, you're going to need to actually write full assembly. Most of the time, whatever intrinsic you would have used, the compiler already knew about. Where you get your power is more often in restructuring your loops to best manage your pipeline (and intrinsics don't help there). It's possible this has improved over the last couple of years, but I would expect the improving vector optimizer to outpace the value of intrinsics more than the other way around.
-O3
, then -ftree-vectorize would already be implied, so I wouldn't expect a change in performance. Additionally, if somebody has already written the code around the bottlenecks near-optimally, I wouldn't expect to see any improvement. The only way to truly tell is to look at some performance data for the code, find the hotspots, look at how they are currently implemented and what they currently compile to, and then take a decision as to whether you can do better. – James Greenhalgh