I have only used Pull to create a 3D mesh from a 2D mesh on a single body part. I don't know what happens when you have a multibody part. Maybe the software is smart enough to share nodes automatically, maybe you have to perform a Mesh Merge. In either case, you won't need bonded contact. If you suppress the Rim and only have the Tire, you can run a Modal analysis and request 12 modes. Don't use any supports in the Modal analysis. You should get a practically zero frequency for the first 6 modes, then a large jump up in frequency at mode 7. This will be evidence that all the bodies in the tire are connected. You can examine the deformed shape animations for modes 7 - 12 to convince yourself that they are working.
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