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You can. This article may help: https://www.gardeningknowhow.com/edible/vegetables/beans/pole-bean-supports.htm

This article will help explain the cross pollination process: https://www.gardeningknowhow.com/edible/vegetables/vgen/cross-pollination.htm

They may have too much nitrogen. This will cause lush growth but few or even no blooms. Try adding bone meal to the soil. This will add phosphorous and help offset the nitrogen.

This article will have some other possibilities:
https://www.gardeningknowhow.com/plant-problems/environmental/plant-not-blooming.htm

This is not required nor proven to make any difference; however, if you’re not careful, you could wind up making the beans more susceptible to diseases. Here's an article that may help: https://www.gardeningknowhow.com/edible/vegetables/beans/tips-for-growing-beans.htm

Greens, being green and leafy, take a lot of nitrogen from the soil. Old time gardeners might not have known about the chemistry involved, but without all that scientific stuff they figured out that legumes fixed nitrogen back into the soil. Organic gardening at its best!

Is there enough air circulation in the greenhouse? If not, it could be due to excessive moisture. Excessive moisture is an ideal environment for the development of fungus as well. If a fungal infection has occurred, this could prove detrimental to the plants. While fungicides are available, timing of the disease is crucial in order to save the plants. Root rot can cause pole bean leaves to turn yellow. To check for root rot, carefully pull out one of your pole bean vines and check the roots. Healthy roots should be white.