Depends on your definition of "axle." If you define "axle" the same way a brake jobber does, then yeah, it connects to an axle. If an axle to you is what drives a wheel, then no, a tie rod does not connect to the axle.
The tie rod is a pivot in the steering system. If the vehicle has rack and pinion steering there is typically an inner tie rod (attached to the steering rack) and an outer tie rod end which connects the inner tie rod to the steering knuckle. The pivot will allow the joint to move up and down and rotate as the steering and suspension move. I'll see if I can find a Wiki diagram that will clear this up....
Try
this one. In the rack and pinion system what I refer to as the inner tie rod the diagram refers to as the "inner socket assembly." The diagrams are not as clear
here but it gives a better description of the systems.
-Rod