Do the actual false colours in the M87 black hole picture convey information? As for the title. The picture could have been plotted in grey scale, B&amp;W, whatever couple of colours, or perhaps using a window of wavelength in order to show shift of the Doppler/relativistic Doppler kind.

Discarding the obvious dark, shall the picture be watch at merely in term of brightness, or considering yellow and red as well? 

And independently, why those colours have been choose?  Just an aesthetic and suggestive choice, or that should be the apparent image as seen by eyes if we could go there? 

I resume: is the picture a radio waves intensity or brightness map, or conversely a kind of "as it would be" picture in the Vis (modelled from the behaviour of the collected radio waves and theories)?
See this article recently published by the EHT collaboration describing how they generated the image. Specifically, chapter 5 of that article describes the origin of the image. To quote the article (specifically the caption of figure 3):


  The image is shown in units of brightness temperature, ${T}_{{\rm{b}}}=S{\lambda }^{2}/2{k}_{{\rm{B}}}{\rm{\Omega }}$, where S is the flux density, λ is the observing wavelength, $k_{B}$ is the Boltzmann constant, and Ω is the solid angle of the resolution element.


The false colors in the image convey the surface T brightness (a sort of measurement of the intensity or flux from that area) of the material surrounding the black hole's event horizon. Brighter color means higher brightness temperature. There is not information about the physical T of the in falling materials as the collected radiation is of synchrotron type and not that of a black body. As you say, the image could have been shown in grayscale or any other color scale. The fact that it is shown in an orange-ish color is merely the convention chosen by the scientists who generated the image.

BUT there's a lot more information in the image than just how bright the material is. For example, the fact that the material is brighter on one side than on the other can tell us about the geometry of the material surrounding the black hole, or about how that material is rotating around it. If you have the time, check out this article and read up on the actual journal articles published by the Event Horizon Telescope collaboration linked at the bottom.