Nearly. I quote from Pop Goes the Weasel: The Secret Meanings of Nursery Rhymes, by Albert Jack:

The Anacreontic Society was a gentlemen's club formed in London during the mid 1700s, by a group of amateur musicians attempting to promote their craft --- in honour of the Greek poet Anacreon (570--485 BC). The membership was known for its "wit, harmony and love of wine". The president of the Anacreontic Society, Ralph Tomlinson (1744--78), wrote the words of a drinking song that he called "The Anacreontic Song" and which was soon adopted as the society's official anthem. The first verse goes like this:

To Anacreon in heaven where he sat in full glee,
A few sons of harmony sent in a petition [ ... ]

And so it went for five further verses, each one encouraging the members to drink more heartily.

The matching tune was composed the following year, and the "raucous lyrics and memorable tune" ensured its propagation "throughout England and America", being folk-processed along the way to suit the occasion. Over forty years later, the incident occurred which caused Star-Spangled Banner to be written.

Hope that helps, folks.

PS: Dear MudElf, do we have the full original lyrics in the DT? I've only got the first verse here.