Thanks Dave, for pointing me to the pathcopy.rb plugin. Works like a champ.
I did a couple of things that helped it work pretty much perfectly.
1) When drawing the curve, make sure to bump up the number of segments by quite a bit. The more segments = The smoother the Curve = the better the objects can be placed on it.
2) Place the components origin in the right spot. For mine, that was right smack in the middle, a little bit back from the front so the outside edges would all mate up.
3) Do the "copy to spacing" option, and specified exactly the width of my component.
This is going to save me a lot, a lot of time...