The speaker of this poem is classic John Donne. That doesn't mean that this is how we would expect John Donne to speak if we saw him walking down the street (that would just be awkward), but this voice is entirely consistent with the voice we hear in much of his work.
Whether he was addressing God, Death, the sun, some lady he'd just met, or his wife, Donne's voice tends to take on a clever, argumentative, even haughty tone. We mean, in line 23, he says that princes are only pretending to be as great as him. It's as if Donne knows he's being clever, or as if he's performing a magic trick and saying, lookee here!
This sort of voice makes sense. Donne's poetry wasn't published in his lifetime; it only circulated among his friends. And his buddies were all upper-middle-class lawyers and writers who hung around coffeehouses trying to one-up each other. The speaker of this poem seems to intentionally go out of his way to make outlandish boasts and bizarre images and then try to make it all work out by the end of the poem.
But hey, we'll cut this guy some slack. He is clearly head over heels for whoever this lady is that's lying in his bed. So we can forgive him his I'm-the-king-of-the-world moments, and write it off as young love. Doesn't it make us all a bit full of ourselves?