I find no Internet references to either Julien Carle or to an 1853 reference to "Here's to Good Old Yale."

The earliest mention, of the title alone, is in an 1866 issue of (ironically) "The Harvard Advocate." The words and tune appear in "Carmina Yalensia" (1867).

In any case, it seems to me more likely that the Yale song came from the drinking song, rather than the other way around, particularly since the Yale song has "balm of gilead" and "bingo" elaborations.

Around 1860 there were far more tipplers than there were Yale students.