It's not clear to me, it seems that you say contradictory things, but if you want an object to follow a path and some copies to follow behind, without deformation, you could:

• Give your first object a Follow Path constraint. Click on the Animate Path button and activate the Follow Curve option.
• Link-duplicate the object as many time as you want (altD then directly press Enter).
• Change the Offset value of the copied objects.

Edit: Robin's solution seems more adequate but here is an alternative.

If you want an object to follow a path and some copies to follow behind, without deformation, you could:

• Give your first object a Follow Path constraint. Click on the Animate Path button and activate the Follow Curve option.
• Link-duplicate the object as many time as you want (altD then directly press Enter).
• Change the Offset value of the copied objects.