Depends where in Florida - Yucca brevifolia grows in USDA zones 6a-8b; Florida is 8a to 11, depending which bit, so if you're in Zones 8, 8a or 8b, yes. If where you are is above that, then no.

https://www.gardeningknowhow.com/ornamental/foliage/yucca/joshua-tree-information.htm

It will also need extreme drainage, especially during the hurricane season. In its native southeastern California and western Arizona, most of the precipitation happens during the winter. It grows in early spring, when the weather is cool, and high heat and humidity make it very subject to certain Phytopthora root rots.
As Bamboo says, a little "bite" in the winter is essential to flower formation and normal branching. They grow well enough here in Zone 9b, but they develop a weird sprawling shape--not like the picturesque trees of old Westerns.
Also when grown away from the Mojave desert, it is necessary to dig up numerous offsets, which are normally eaten by an endemic beetle species in its native habitat.

Interesting extra details there, Tug - particularly the endemic beetle bit, fascinating.

Yes, the more natural science I learn, the more I realize what a fractal, three dimensional bit of Venetian lace Nature is.