Your case might be somewhat uncommon, but I think a more common case to be considered is when people specifically try to hide their original accent/dialect in order to 'fit in' more with the people they're speaking to. In a lot of cases, this is seen as duplicitous; if you're trying to hide how you really talk, then what else are you hiding about yourself? Can anyone really trust anything you say when you're deliberately saying it in an unnatural way?
In terms of cultural appropriation, normally you aren't the one who gets to decide if you're part of the culture; culture is a communal experience, it's created by groups rather than individuals. Birthright often isn't enough, and claiming you're part of a culture because of your ancestry can even be taken as an offense. Basically, in many cases, membership in a culture isn't born or bought, it's earned. This is why 'poser' is an insult.
So I'd say the only way it would be appropriate for you to adopt another accent/dialect is to earn it. If you steep yourself in the culture for long enough, some of it is bound to rub off on you, especially if you let it. If you let Appalachia become a part of you, then your claim to its culture will be stronger, and you won't be lying to people by using its accent.
Of course, you could also just do what you want and not worry about what people think of you. That's a valid option, if you're not concerned about losing friends or making enemies. Other people's opinions shouldn't dictate how you live your life, unless you want them to. I wear skateboarding shoes because I like how they look and feel, actual skateboarders might think less of me for it but that's a risk I'm willing to take.