Globalized mass-media deterring language or dialects differentiation

The problem with the question as posed is that it cannot be easily answered empirically. Dialects are subject to many more processes than simply exposure to media. They have been nivelized long before the presence of mass media. English appears to be in a state of dialect leveling at the moment but that is as much a result of politics as media. They just happen to be happening at the same time.

(Mass) media can be just as much agents of dialect differentiation as disappearance. For instance, local mass media can give a dialect a legitimacy it would otherwise lack or even result in the creation of new languages. For instance, the constant tug of war between Croatian and Serbian could over time result in the transformation of dialect into language - mass media are as likely to support as inhibit this process.

Plus the process you describe (i.e. the dialect of the center serving as the foundation of an ever expanding standard) has happened long before the presence of mass media. You could say the invention of the idea of a nation state had even more of an impact. A century and a half ago, Czech and Slovak all consisted of a continuum of dialects and it would have been easy to create one standard against which all the dialects would be measured. But due to political influences, this did not happen. Things like literacy and media were used as tools in achieving this outcome but we not just some passive presence that played a role in either direction.

So in any individual case, mass media cannot be predicted to have one result or another. However, the case could be made that overall the presence of unifying communication platforms (literacy, media, internet), the number of dialects decreases as more 'standards' are established and promoted. But these things haven't been around for long enough to be able to say. We don't have good enough records about the past across languages and cultures to have enough data and it is very dangerous to extrapolate from the current state.

It may also be worth bringing up the 'punctuated equilibrium' thesis which RMW Dixon adapted from biology to language. Which could just mean that the apparent slow down of language change some people posit is simply a temporary phenomenon.