Christopher Marlowe's poem only reveals the passionate shepherd's point of view, so we don't really have any textual evidence of whether he was successful or not, but we can look at his approach and judge for ourselves how effective is persuasive techniques are.
The poem, as a whole, is very a very optimistic and ideal vision of pastoral life. The speaker says that if the young lady would join him "we would all the pleasures prove." He goes on to describe the beauty of nature, specifically the flowing rivers and the melodious birds. He promises her a bed of roses and fragrant posies. She could have a garment of flowers and fine wool and shoes with gold buckles. She could have "coral clasps and amber studs." The last image he paints is of other shepherds dancing and singing their delight. All of this sounds very inviting, but the reader has to realize that the life of a shepherd is anything BUT easy. It is a very lowly and lonely job, with exposure to the elements and a lot of boredom. In reality, a shepherd could never afford any luxuries, much less gold, amber, or coral. In the end, this passionate shepherd is using very pretty imagery to make promises that he could never keep. It would all be convincing only if the girl wanted to be wooed with words knowing that the actuality of life with a shepherd would be filled with hardship.