Ok...
Can a replicator's shapes individually conform to a motion path? As you've likely figured out: no.
By your question, I've been assuming you want each copy of your image/object to appear, start moving along its Motion Path, then have another appear at the start of the Motion Path to follow the previous one, etc...
The only way I know how to do that is to create your animation with one object, then duplicate the object as many times as you need. Select each object's layer in the Video Timeline window and drag them to a slightly later starting time, like this (only showing 3 objects):

You will have to adjust the length of your project to accommodate the animation of all your objects.
You can't use clones because they are a "flat-screen projection" of the animation and you will lose 3D capability.
Replicators will always spread out the copies of your objects along the "path" you use. Emitters have a problem with 3D position as well as randomly using some position along the path to start an object's animation.
There are some Replicator options that might make a suitable alternatives.
Replicate your image.
Set the Shape to Circle and Arrangement to Random Fill. Radius to about 600 or so (very flexible). Points to 30.
Check 3D and Face Camera.
Adjust Scale if needed.
To the Replicator, add Behaviors -> Simulations -> Orbit Around. Set the Strength to set the (fastest) speed of animation (start at about 1500) and use the Falloff Rate to the get the animation speed you like.
Influence determines how far away an object is that will receive the Orbit animation.
Then for Include, select X and Z... and the Direction of spin you want.
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Here's another idea... and it uses the spiral path you designed:

Replicate the image. Set the Shape to Geometry and add your path shape. Set the number of points and to the Offset, apply a Ramp behavior [End Value = 100%]. Check 3D and Face Camera. [Adjust the Scale to taste.] In Transforms, set the X Rotation to make arrangement look similar to the image [mine is set at -49º].
You can create gradient masks for the beginning and the end of the path so it appears the images are moving in and out instead of jumping to the beginning of the path.
You can create Rectangle shapes and size them to match the first and last images. Set them to B&W gradients. Move them in 3D space to match the first and last images and then set their Blend Modes to Silhouette Luma.
You need to have the angle of view [the Rotation I mentioned] set up so that the mask rectangles won't overlay any of the other animating images.
PS - I have the Replicated image Cropped so that they don't cross through each other as they move...
Have fun! :D