Well, yes. Sometimes!

Box Canyon Road in the southern Mojave Desert, in a place that gets only a few inches of rain a year--with most arriving in a single storm! The tree behind the sign is a palo verde (Parkinsonia spp.), a typical element of the Mojave flora in this area, with its range also extending east into the Sonoran desert. The name means "green stick" in Spanish and is due to the fact that the leaves are vestigial, with all the chlorophyll occurring in the trunk and twigs. It's presumably an adaptation to minimize water loss. The inset shows another individual.