Dipole vs. charge
Firstly, one needs not a dipole - a single accelerated charge would emit electromagnetic waves - see Liénard–Wiechert potential and Larmor formula. The point of using dipoles in models of antennas is because a dipole (like an antenna) remains overall electrically neutral - it however adds nothing to the ability of charge to radiate (or might even reduce intensity of the radiation.)
Accelerated charge
That an accelerated charge radiates is known, e.g., from a phenomena like Bremstrahlung (this is also the case of simple antennas, but the fact that the accelerated electrons move in the wires adds a level of complexity.)
Rotating charge
Then, if we want radiation from charges that actually rotate - Synchrotron radiation is a ubiquitous phenomenon - from particle accelerators to microwave ovens.
Problems with do-it yourself stuff
However, I realize that the question is more about engineering, material science, and do-it-yourself experimentation - can we actually attach a charged sphere to a hard physical stick and observe radiation? The problem is that one needs to rotate stick fast enough to actually observe something. As we know 50-60Hz power outlets hardly emit noticeable electromagnetic radiation, because the attenuation length is shorter than wavelength, and we cannot observe the radiation from far enough to see it as a wave independent from the source (although the gossip goes that one can have enough power, if using a power network of a whole country, and that attempts were made to use it for communicating with submarines under water, where the electromagnetic waves are attenuated even stronger.)
So one would need a stick that we could rotate with kilohertz or even megahertz frequency. I admit that I do not answer this question - but, as I have pointed out above, it belongs to engineering and material science, as there is no physical principle that such an experiment could confirm or disprove.
Update: about scientific theories
In view of the discussion in the comments, it is worth adding a few remarks regarding the status and interpretation of scientific theories, notably the Electricity&Magnetism, as described by the Maxwell equations.
Importance of theory is not only in what it includes, but also in what it ignores
What is included in theory is usually obvious from the variables included in the equations and the form of these equations, as well as from the assumptions of the theory (easily overlooked in "plug&calculate" approach, but nevertheless usually stated in textbooks.) What is not included in the theory is less obvious - not in the least because the number of the ignored parameters is potentially infinite. A physicist is fairly sure that the result of an experiment in E&M is independent on who does the experiment, the personal beliefs of the experimentalist, the politicians and power, etc. (Although on some occasions scientific theories were indeed deemed incorrect on philosophical grounds - notably genetics in the USSR.)
It might seem less obvious is whether we can ignore, e.g., whether a charge is rotated by an actual physical stick or by a Lorentz force, as in a synchrotron. However, we known that E&M is a local theory - we know that how the charge behaves is determined only by what happens to the charge itself, not by its surroundings. What may happen in a problem with a stick is that the stick is affected by the EM field emitted by the charge, and emits its own field, e.g., amplifying the field emitted by the charge. Indeed, this is precisely the case with the paper Amplification of electromagnetic fields by a rotating body, cited as the motivation for the bounty award. I quote its abstract for further discussion:
In 1971, Zel’dovich predicted the amplification of electromagnetic (EM) waves scattered by a rotating metallic cylinder, gaining mechanical rotational energy from the body. This phenomenon was believed to be unobservable with electromagnetic fields due to technological difficulties in meeting the condition of amplification that is, the cylinder must rotate faster than the frequency of the incoming radiation. Here, we measure the amplification of an electromagnetic field, generated by a toroid LC-circuit, scattered by an aluminium cylinder spinning in the toroid gap. We show that when the Zel’dovich condition is met, the resistance induced by the cylinder becomes negative implying amplification of the incoming EM fields. These results reveal the connection between the concept of induction generators and the physics of this fundamental physics effect and open new prospects towards testing the Zel’dovich mechanism in the quantum regime, as well as related quantum friction effects.
We need not test a physical theory in all possible situations
Firstly, testing E&M in all possible situations is an impossible task - even with a charge on a stick one can think of an infinite number of situations: a stick can be from metal, wood or plastic, it can be red or blue, it can be one, two or hundred meters long, etc.
Moreover, testing theory for all possible combinations of relevant and irrelevant parameters would defeat the very purpose of the theory: to make predictions for new situations on the basis of the few known ones. The paper in question is an excellent example of this: Zel'dovich made a model calculation, using standard Maxwell equations and related theories. This calculation was never intended to be a test for the E&M - in this sense it was not a science, but high level engineering (I hope that no one is offended by my drawing such a division between science and engineering, as discovering new laws of physics vs making predictions on the basis of already known laws.)
Although the experiment was not possible in 1970s, the result was never in doubt. That we can do such an experiment today is an impressive technological achievement, demonstrating state-of-the-art technology available only in physics labs so far... yet the achievement remains technological rather than scientific - just like sending people on Mars would be technologically impressive, but in itself does not constitute new science.
Nowadays such technological achievements are often made in Universities and research centers, and even awarded prizes - like the discovery of graphene (this was mostly technological, although one could claim that showing that graphene was a stable phase of carbon was indeed a scientific discovery.)
To summarize: observing radiation from a charge rotated on a stick, as technologically impressive as it is, does not question the laws of electricity&magnetism, and conceptually is no different from rotating charge in a synchrotron.