I would say that it depends upon:
1. your own accent
2. whether or not you have an ear for accents,languages etc.
3. the dialect/language of the song(s) you want to sing.
To 1:- the radio programme about The Critics Group included one of them singing "The Strawberry Roan"....unfortunately in a plummy upper class english accent- and no, it wasn't a piss-take. I had a serious fit of the giggles! There is perhaps something to be said for recording yourself and listening critically to the result. My own accent could be described as BBC/standard RP but years spent in Derby, London, Swansea and Lancaster have enabled me to tone down any tendency towards 'pluminess'. On the other hand, as a voice-artist, if a client wants 'pluminess' then he'll get it, but that's a different ball-game.
To 2:- I've been living in Germany now for over 30 years and so speak german reasonably well. However I have an english accent. Hearing the, often cringeworthy, attempts of many Germans to sing in english makes me wary about singing in german (or french or swedish for that matter)- I can do it where necessary (e.g. "La Complainte du Partisan"), but I don't make a habit of it.
To 3:-(overlapping with 2) Generally I find that scottish and irish songs, including the ballads, to be no great problem. I may 'anglicise' the pronunciation of a word here or there, it depends principally upon the rhyming scheme and whether I feel that the story will or will not suffer in some way. For example, I occasionally sing "The Blackleg Miner" but with 'don't' rather than 'divn't'( go near the Seghill mine) and I don't feel that this change detracts from the story. As far as the 'big ballads' are concerned, there are so many versions of the individual stories that it's no great problem to find one which presents only minimal linguistic challenges and yet satisfies. On the other hand I wouldn't even contemplate singing songs such as "John McClean March", "Freedom Come-all-ye" and "Banks of Sicily" precisely because those songs stand and fall with the language and for me, although I'd like to think that I have an ear for languages and accents, I don't feel that I could sing such songs convincingly- and that is perhaps the point.