If you can’t be bothered to read the following paragraph, the short answer is: No (in my opinion).
Below is a picture that we did not include in our recent paper about the “neutrino question”, but which is a summary of my views.
First, it illustrate again the well known tension between the Planck measurements of the primary CMB and the abundance of SZ-detected clusters, in the context of the standard LambdaCDM model. It is also apparent that adding neutrino masses and extra-relativistic species (mnu and Neff parameters) to the model, i.e. considering massive active or sterile neutrinos, does not resolve this issue. For them to resolve the issue, you would need the black and grey contours to overlap as the model is extended. Yet, even when adding these parameters, the Planck SZ and CMB measurements are still excluding each other at many sigmas.
The recent claims of massive neutrinos arise from combining these measurements despite their disagreement. If you do so, you will obtain a compromise “best-fit” model somewhere in the middle, indeed favouring massive neutrinos, as indicated by the coloured points. However, this new model is ruled out by its individual ingredients…