As a performer there are simply occasions, as trevek says, when adopting a 'foreign' accent is appropriate. As a teacher of English for many years I had to read to and with pupils. One favourite book of both pupils and teachers was Robert Westall's 'The Machine Gunners'
set in WWII Geordieland. It contains lots of great Geordie dialogue and a smattering of Glaswegian. Having watched an accompanying video many times the accents were easily imitable, and so to make the reading more enjoyable and more realistic I adopted the appropriate accents. After the initial shock/giggling had died down and the pupils got used to it I encouraged some of them to attempt the accents as well and some of them became quite good at it.

Also many of my friends are Geordies and I spent a lot of time up there in the Holy Land. I picked up a lot of the local music hall songs, Blaydon Races, Cushie Butterfield, Lambton Worm, Keep yor feet Still, simply so I could join in. My best mate was a great concertina player but couldn't sing a note, so if the two of us were out in the pubs I would do all the singing. I even ended up learning some Northumbrian ballads just to please him. Needless to say I used the local accent and I don't ever remember any of the locals complaining.

Having said that, although I know a lot of the muckle sangs I would never sing any of the Scots ones in public. The only Child ballads I sing I sing in SE, unless you count that remnant of The Elfin Knight 'Acre o' Land' which is sung all over the East Riding and has its own dialect versions.