I need help with the analysis of the poem "The Mower's Song" by Andrew Marvell. Is a political interpretation of this poem possible?

To begin, Andrew Marvell lived and wrote in the 17th century, and his political views shifted throughout his life and career. Particularly in his later works, Marvell was somewhat critical of the rigidity of the established church and royal court of England.
"The Mower's Song" is a poem about unrequited love, but it is not only a poem about a broken heart. The mower is at odds with the classic English meadows; he suddenly resents them and the brutal manicuring he does to them as the mower. This correlates to Marvell's resentment of the self-indulgent, formal, and materialistic nature of institutions. Just as the growth of the meadow is impeded by the destructive mower, so too is progress impeded by the stodgy values of church and royalty.
Consider the following lines from the poem:

Unthankful meadows, could you so 
      A fellowship so true forgo? 
      And in your gaudy May-games meet 
      While I lay trodden under feet? 

Extracted from the context of Juliana's cruelty, these lines seem quite political indeed. Essentially, when the speaker asks, "And in your gaudy May-games meet / While I lay trodden under feet?" Marvell asks the reader, "How can the established institutions revel in their formalities while England suffers from a lack of progress?" Just as Juliana scorns the poor mower's love and the mower tramples the grass for his work, the English establishment thwarts the nation's ability to embrace modernity.