But would her British accent by forgotten and would it be so bad if she sounded American? Well, that gives us American a lot to think about doesn’t it? We’re not good enough for Sir Paul McCartney then?!
Most English-speakers speak with an American accent. If you want to be a little exotic - and doesn't everyone - you have to speak with an alternative. Upper-class British is as prestigious as they get.
Likewise, if you listen to American bands you will sing with an American accent, because that's what you're used to.
You can, but you don't always. It depends on how closely you mimic the style. There was a big debate in Aussie hip hop during the last decade over accents. Some groups rapped with American accents, some with Australian ones.
I don't think either one actually won the debate, but there's no doubt the Australian-accented groups have had more success domestically.
An accent is sometimes an expression of cultural solidarity. Those who felt more at home with the American cultural notions behind American rapping tended to use an American accent, those who felt more of the Aussie vibe tended to rap with an Australian accent.
Off-topic:
Personally I prefer Aussie hip hop to anything coming out of the US. It's way more laidback and fun. On a sidenote if you want to check it out have a search for pretty much anything by the Hilltop Hoods, but 'Fridays' by Matty B is also a great Friday song (funny that!). If you're into political rap the Herd are pretty awesome, especially their track 'I was only 19', which is a cover of the old Redgum classic.