Yes, that's perfectly possible; though the song was printed in the USA more than once in the mid-19th century. In this case it's reasonable to class the Utah text as a discrete Utah variant. The information EJ and I provided earlier (the posts are presently out of sequence, of course) was incomplete. I now have access to more complete references (though not at the moment to the JAF piece itself), so I'll enlarge a little.

The text I quoted was from James Jepson (Hubbard printed it as The Hard-Hearted Young Man) but there was no tune. The tune actually belongs to another Utah set printed by Hubbard and Robertson, and reproduced in Bronson I 340 (43.11): this was from Salley A Hubbard (aged 86 at the time), Salt Lake City, Utah; she had learned it from "Doc" Lish, Willard, in 1871.

Both texts are similar and both refer to the "May blooming field", so would appear to be forms of a variant circulating in Utah in the early 1870s (wherever it came from before that). It's reasonable to think that the tunes will have been alike, but we don't know for sure, so my earlier comments on the tune should be taken as tentative only; it isn't clear whether "Cordelia's Dad" used the Hubbard tune in their arrangement (which I don't think I've heard) or added one of their own.

The song is surprisingly rare in the USA considering its popularity in England and (to a lesser extent) Scotland over some 300 years. At the time Bronson wrote, he knew of only one example found in America with a tune, though a few others have turned up since then.