Ask Mr. Smarty Plants

Great question! Even though these two great native shrubs have "bean-like" seed pods and look something like the legumes, the group of plants (Fabaceae) that fix nitrogen through symbiotic bacteria within the nodules in their root systems, they do not perform this important function.  There are a small group of plants that aren't in the Fabaceae family and these include tropical parasponia, hardy alder and bayberry, a few plants in the Rosaceae, Rhamnaceae and Elaeagnaceae family.

By the way, the following is information from the Lady Bird Johnson Wildflower Center about your two Bignoniaceae shrubs:

Tecoma stans (yellow bells) Esperanza or Yellow bells is an irregularly shaped, deciduous shrub, normally 3-6 ft. tall in the US but more southerly varieties can reach 9 ft. It has several stems and slender, erect branches. Clusters of large, trumpet-shaped, yellow flowers are very showy against the lance-shaped, olive-green leaves. Long, thin pods are conspicuous in autumn. It has an enormous natural range, extending from south Texas west to Arizona and south through Mexico and Central America to South America as far as northern Argentina, as well as in southern Florida south through much of the Caribbean. Plants native to the southwestern US and adjacent Mexico are Tecoma stans var. angustata, which is shorter, more drought-tolerant, and more cold-tolerant than some of the tropical varieties sold in nurseries.

Chilopsis linearis (desert willow) Desert-willow is a 15-40 ft., slender-twigged, small tree or large shrub, often with leaning, twisting trunk and open, spreading crown. Leaves are deciduous, willow-like, light green, both opposite and alternate, 4–12 inches long and 1/3 inch wide. The blossom is funnel-shaped, 1–1 1/2 inches long, spreading at the opening into 5 ruffled, petal-like lobes. The flower is dark pink or purple, often with white or yellow and purple streaks within the throat. The catalpa-like flowers are borne in terminal racemes. By early autumn, the violet-scented flowers, which appear after summer rains, are replaced by slender seedpods, 6–10 inches long, which remain dangling from the branches and serve to identify the tree after the flowers are gone.