I will start by saying that Wikipedia does not constitute a "good paper" in that not only is it not peer reviewed, but it also can be edited by anyone regardless of their knowledge on the subject, as I am sure you are aware.
Anyway, my first two paragraphs make perfect sense if you understand what turbulence is, or at least where a shock comes from. In fact, except in very specific cases, shocks have absolutely nothing to do with the boundary layer at all, which is the only thing that the terms laminar and turbulent apply to. As an example, the shock wave that forms in front of a capsule re-entering the atmosphere doesn't even intersect with the surface, instead forming what is called a bow shock. At no point does this bow shock even interact with the boundary layer, so whether it is laminar or turbulent is irrelevant.
Back to shock waves: shocks arise any time the flow needs to make an abrupt change of some sort, typically in pressure (see, for example, a
shock tube) or if the flow needs to make reasonably abrupt changes in direction (see, for example,
oblique shocks). Shocks represent near-discontinuities in the flow across which the properties (pressure, density, temperature, Mach number) change dramatically. The most common reason for their formation is when an angular object moves through a gas (or gas moves over the object) faster than the speed of sound, the physical situation dictates that the gas experience a discontinuous change in direction. This is true even in inviscid flows (in fact, that is how they are typically treated), meaning that not only do they not depend on the state of the boundary layer, but the terms "laminar", "turbulent" and "boundary layer" don't even have meaning in the context in which shocks are typically discussed.
Turbulence, on the other hand, is the result of tiny fluctuations in the incoming air flow interacting with the surface of the flying object to form small disturbances in the boundary layer which are them subject to instability. Some die out and others grow so large that they break down into turbulence.
So I will start next by doing a little bit of inserting my foot into my mouth since I apparently just invent the number 2 out of nowhere.
Revolutions per second:
292 \frac{\text{rev}}{\text{min}} \times \frac{1\text{ min}}{60\text{ sec}} = 4.8\bar{6} \frac{\text{rev}}{\text{sec}}
One revolution covers the distance of one circumference, s, so:
s = \pi d = 14.63\pi = 45.96\text{ m}
4.8\bar{6} \frac{\text{rev}}{\text{sec}} \times \frac{45.96\text{ m}}{\text{rev}} = 223.68\text{ m/s}
So yes, you were correct in that the Apache tips don't typically go supersonic. I apparently somewhere inserted a factor of 2? No idea where that came from since there isn't any place for a 2 to naturally occur. I have no explanation for that. I know that 292 rpm is not the maximum rate of spin for the rotor, but I don't have a good source to take this example further. I do know based on NASA documents that there has been quite a bit of work to try and reduce the region of supersonic flow over rotor tips, but that can occur even if the tip itself is still subsonic.
Based on a quick search of several other helicopters, it seems like the trend is for the tips to stay under Mach 0.7 while stationary, which would tend to give it a cushion to push up against but not pass Mach 1 during forward flight. Even at full forward velocity, the Apache would only reach about Mach 0.94, though this is easily enough to have supersonic regions over the blade tips.
I will say, however, that while it doesn't appear that helicopters are designed to allow supersonic tips, that doesn't make it impossible as much as impractical. A properly designed tip could certainly safely pass Mach 1, it is just a matter of whether that buys you anything. I suspect it probably doesn't, but I am not a helicopter guy.
I am reasonably certain I never said the rotors would make a noticeable sonic boom if it managed to be supersonic; only that they can and do move supersonically - a fact which I have now retracted as I don't have definitive. The point is, though, that there is no such sonic speed limit inherent in the concept of a helicopter blade. The issue is whether or not modern blades are designed to support that and whether it would confer any kind of benefit.
At any rate,
assuming you did have a supersonic tip the only reason there wouldn't be a sonic boom is because of how light and thin the blades are and the fact that they are only barely supersonic. They would still create shock waves emanating from the tip region and, depending on the airfoil design, there could even exist the leading and trailing shocks characteristic of supersonic aircraft. In other words, you could presumably still get the N-wave pattern under certain circumstances. The shocks are just going to be very weak and therefore not have a large sound associated with them. You could probably still put a microphone near the blades and catch what are essentially tiny sonic booms (sonic squeaks?) if you wanted to. The only real trick would be discerning that from the sounds of the ordinary blade passing frequency. It would be easier if it did, in fact, have the N-wave profile.
While I won't comment any more on helicopter blades, as I think I have beaten that to death for now, I will say that, without any shred of doubt, turbofan blades do go supersonic. For example, the Rolls-Royce Trent 900 that powers the Airbus A380 has a fan speed of 3300 RPM and a fan diameter of 2.9 m, which translates to Mach 1.46. In fact, at full power, that puts the entire outer third (radially) of the fan above the speed of sound! The difference between this and the blades on a helicopter is that fan blades in a turbofan are much more rigid and designed specifically to do this.
Going back to the previous example, if you were to put a pressure transducer or a microphone close to the blades and analyze the signal, you absolutely
could record many sonic booms. In fact:
3300 \frac{\text{rev}}{\text{min}} \times \frac{1\text{ min}}{60 \text{ sec}} \times 24\frac{\text{blades}}{text{rev}} = 1320 \text{ blades/sec}
This shows that if you stick your sensor up next to the fan disc, it will record 1320 blade passes per second. Whether each has a sonic boom associated is largely a matter of semantics. It would certainly have a shock emanating from it and that should would register on a microphone in the form of sound. Now, it wouldn't likely have the classic N-wave simply because one of the shocks from each blade would be impinging on the adjacent blade most likely, so you would probably only get the single shock passing. The sound itself would also be incredibly small, especially compared to the rest of the engine noise.
