When I sing a song I learned from a record or a person, I tend to try to make it sound like what I heard. Sometimes that's musical, and sometimes that's accent. I know that when I went to England with my sister, it played merry hob with the way I pronounced vowel sounds for weeks, because we started in the south of England and then went north in stages to Scotland. I wasn't trying to "put on" an accent consciously, but I did find myself saying "aboot".
I think Scabby Doug hit a good compromise when he pointed out that vocabulary should stay the same, but that we shouldn't make exaggerated changes to words that we normally use unless we need to to make the song scan right.