Having read Marvell's "The Passionate Shepherd to His Love," (and "To His Coy Mistress"), and reviewing the eNotes summary for the poem, it seems, indeed, that this is a poem not so much about love, but about lust.
"Come live with me and be my love" does not suggest that the couple marry. It suggests that they live together as husband and wife, but not BE husband and wife. The shepherd is basically presenting his "resume" of the advantages of joining him if she agrees. It seems she needs some encouragement because the shepherd spends a great deal of time listing all the things that will be hers if she takes him up on his offer.
They will enjoy nature, and even the birds will serenade them with "madrigals," (songs). He will surround her with flowers: as beds or in the form of bouquets. He will dress her in lamb's wool and make other closes from the plants of the countryside. And all the shepherd's swains (friends who are also shepherds: modern dictionaries may not catch this) will dance for them.
All of this the shepherd promises, if she will give up her virtue (and reputation) and live with him. His ideas may sound romantic, but it's not love on this man's mind.