Our accents do adjust based on what we're exposed to. It's a natural part of speaking a language, and this happens every day to subtle degrees based on the specific people we talk to in a temporary way, and over longer periods of time can be more obvious or even lead to relatively permanent shifts.
There's a great book about learning a second dialect, which basically summarizes the research as showing that it's like learning a second language: more likely for children, less likely for adults, and overall a gradual process following similar steps.
Siegel, Jeff. 2010. Second dialect acquisition. Cambridge: Cambridge University Press.
https://doi.org/10.1017/CBO9780511777820However, that's more about
interaction and communicating in a second dialect or different accent, not just hearing it in movies, TV, etc. Our "ears" adjust more rapidly, and more flexibly, than our "mouths", so to speak. And although there are feedback loops, it would take a lot to really shift to another accent just from hearing it a lot,
assuming you are more often hearing your local/original accent.
The other crucial factor is sociolinguistic, and specifically
prestige: does the speaker perceive the accent they are hearing via media as "better" than their own, or desirable in general? Is their own accent stigmatized? Do they want to be like the people they see on TV? (I imagine, for example, actors might be more likely to shift how they speak, even intentionally, based on what they see on TV, if they want to also be on TV themselves, just as an example.)
So overall it's somewhat complicated, but I would caution against phrasing like "too much media content" or in general thinking of this as something like a disease you can "catch". It's really not like that, but more about social interaction, attitudes, and, yes, exposure, but also practice, and what else is going on in someone's life beyond what they're watching on TV, etc.
Another interesting topic to look up is
categorical perception, which is what allows us to hear individual sounds (technically phonemes, but roughly something like letters in spelling) from the widely varied input from different speakers around us: those categories are crucial for dividing the vibrations in the speech signal into meaningful content, but they're also socially flexible so we can hear different physical sounds as the same category across different speakers. That's how we understand different accents, basically mapping from input sounds to perceptual categories. And with some practice listening to individuals (for example, speakers of Australian English) we get better at it.
Eventually, yes, we might start to be able to produce it, although it takes a lot of exposure, and also generally a
lack of continued exposure to our original accent. Sometimes speakers can end up "between" accents, if they move somewhere else and start gradually shifting toward the new accent, so they don't sound exactly like their original accent or the accent of their new location, and if they move back and forth, it can fluctuate between the two.
Here's an article with some technical research on the topic. The ideas are clear enough, although the terminology is technical regarding exactly what is being measured.
https://doi.org/10.1006/jpho.1997.0051(I don't know if anyone has tried to measure something like that correlated to how much foreign TV someone watches, or anything like that. I imagine there might be very small effects that would be very difficult to measure, and probably not perceptually relevant for others around them.)
