No, Joints are inherantly transforms.
When a joint is made what you see is a visual representation of its transform position and orientation.
It does not have a local pivot space which is what is edited when you move a pivot.
When you move the 'pivot' of the join all you are doing is moving the selected joint (in actuality you are moving all the joints down the chain!, look at the tanslations of of the joints down the chain the move the 'pivot' of the one before and then look at the orignal again you will see that the transforms have changed ... the children joints are positioned relatively to the parents)
To get the effect of moving the pivot you can either parent the joint to somethign else (only really works as you want I guess if its the root joint) Or parent constraint, though this might screw up your rotations. This is fine depending on what your doing, it has the potential to really make things behave strangely and you will run into gimbal lock pretty quickly if your not careful.
Ill explain incase anyone is interested in the geeky stuff:
In a mesh verticies are placed as a displacement from an objects transform, and when you move the pivot all you are doing is moving a local pivot relative to the actual one.
To see this:
make a cube move it up ten units... the actual pivot point is now +10 in y, notice when you move the pivot around or modify the mesh and centre pivot that your translate y is still +10 in y, all that you are doing is moving the local pivot relative to the original which is allways there and does not move.
If you go into the attribute editor of the transform node you can see this again if you go under pivots> local space and zero everythign out there, it will go to exactly where it was originally.
So in a hierachy what actually happens is something like world space matrix(0, 0, 0)> object matrix (always relative to its parent, by default this is world) & local pivot which is again relative to world (you can see this because whenever you move the pivot (hold d key) its axis always align with world space> tanslation is performed on local pivot which then modifies the actual object pivot.
FX supervisor - double negative