Of course. Australian Galahs speak like Australian people. The birds aren't actually learning words, they're mimicking sounds. An accent is the sound of a pronunciation. If a parrot is only mimicking sounds with no understanding, it would of course, mimic the accent.
They mimic, so they sound like who (or what) they're copying. Some, especially African greys, really can be eerily exact. A woman I knew had a grey that copied a burp and "excuse me" it picked up from a guy. The bird could be just babbling nonsense as she and I talked, then -- burp, excuse me -- and I'd look around for the person!
Only to an outsider. Fun fact! Crows have developed a language, it is so ordered that there are actual dialects depending on the crow's location. ie a crow from California sounds different than one from Newfoundland. http://www.cracked.com/article_19042_6-terrifying-ways-crows-are-way-smarter-than-you-think.html
If they are learning the language of the land, I guess they say the words with the natural accent being spoken by the people teaching them.
Not to their original owner
You only have "accents" when you speak in a language other than your native tongue. So the answer is no.
Things that make you say Hmmmm??? lol
Do all of them speak?
why don't you ask one?