Well, in the specific case of British ballads in the Southern highlands, I think the textual evidence supports the conclusion that these ballads and songs were brought to North America pre-nineteenth century. There is great deal of variation from British broadsides in the Appalachian versions of popular ballads such as "Gypsie Laddie", etc. Instead of "milk white steeds" you find mules, for example. So you can conclude the ballad has been in the oral tradition for some time. You wouldn't mistake a North Carolina variant for a nineteenth century stall print.

Nineteenth century Irish broadsides in North America (circa early twentieth century) are generally closer to print versions simply because they aren't quite as old, and they are more likely to have been learned from print or from stage performers using print sources.

So the degree of change in a text and the degree changes reflect local conditions can at least tell something about how long a song or ballad has been known in a particular region. Not quite the same thing as positively dating a song, I know.