The biggest problem is being able to plant it close enough to your trees so that it can climb up them. Where you are this plant is only an annual, as it is in the UK, and reaches about 2.5 metres in a good year, but you can't plant too close to the roots of the trees because it will likely be deprived of both water and nutrients, you'd need to plant at least two feet away, in front of the trees. You could plant in a pot and stand near the trees, but it won't get so large as it would in the ground, and given the height of your trees, may well look a little lost amongst them.
The other problem is, this plant is a twiner, and many conifers are really quite difficult for such a plant to twine around - petiole or tendril climbers such as clematis have an easier time of it in that regard. You'd probably need to provide long canes for the stems to twine around, which I'm sure isn't the effect you're looking for.