Does Allegro have some way of enabling backface culling?

https://www.khronos.org/registry/OpenGL-Refpages/es2.0/xhtml/glCullFace.xml

?

No, but we could add it: https://github.com/liballeg/allegro5/issues/942

Got my vote.

Mine too - shouldn't be too tough to implement for both graphical backends.