As it happens, I've done this before. A friend of mine illustrated one of my poems for a comic anthology. That was a lot of fun.
I also studied comics a lot when I was working on some relevant projects, so I learned a great deal about how they work and how to make the words for one.
With that in mind, some answers to questions from the post:
Is the artwork an illustration of the words, or an equivalent to a line of verse or a stanza?
Typically, the artwork is an illustration, as the text of a comic is usually written before the art.
If the poet removed the artwork, would the poem be incomplete?
Usually not if the poem was written first.
It is possible for a comic to emphasize the words, or the art, but usually it's a balance. So if a poem were written intending to turn it into a comic, with half the weight of information carried by the art, then it might very well be clearly incomplete with only the text.
Would the illustrations make sense without the words?
A good comic usually does make sense without the words, even if much nuance is lost. Consider the popularity of manga even if they are not translated.
Can pictures rhyme?
Rhyme is just repetition, so yes, pictures can rhyme. Look for consistent, repeating motifs. This could be done with any of the basic aspects of art -- shape, color, composition, character, and so forth. I think a good visual rhyme scheme could be made with the landscape line rising and falling.