To give a specific example of a case where the question may apply:

I know of at least one performer who's set Rudyard Kipling's "Smuggler's Song" to music, and there is a couplet in the refrain for that verse to which the dialect/accent issue seems to me to apply:

"Five and twenty ponies, trotting through the dark;
Brandy for the parson, baccy for the clerk;"

Now in modern American English, we pronounce "clerk" as clurk, which is at best a half-rhyme. But my sense of Kipling's English is that he would have spoken the word as clahrk (as we pronounce the name "Clark"), which is both a better rhyme and more appropriate to the time and place reflected in the lyric.

So if I were singing or reading that line in a performance, I'd use the clahrk pronunciation, which reflects the (now, at least) slightly archaic and specifically British dialect in which Kipling wrote.