Does saving as a cloud document break the sync between PS and LR?

I am still learning the Creative Cloud Sync system. 
So I have an image in LR Classic Desktop.  I open it in photoshop desktop, edit it but then save it as a cloud document so I can edit it on my iPad as well.  It all works well on the iPad, I clean up some of edges on the couch, save my file, then open it up again as the cloud file on Photoshop Desktop. 
But when I save from the desktop, the end file will not save back to LR. 
Is this normal?  Am I doing something wrong and does saving an image as a cloud image in photoshop break that link between lightroom? 

By @Morningland

An Adobe cloud document does not exist anywhere on your computer, except for being temporarily downloaded when you edit one. A cloud document cannot be found by looking through folders on your computer, and cannot be found using the OS search feature in macOS, Windows, iOS, or Android. Cloud documents can be found and opened only through the Home screen on Adobe desktop, mobile, and web apps.

Lightroom Classic is fully based on local storage of originals. It always looks for files on your computer (and attached storage such as mounted external volumes) only. Lightroom Classic maintains no links to Adobe cloud documents, partly because they are not local. If you compare those conflicting ways that local and cloud documents are stored, it is impossible for a Photoshop cloud document to appear in Lightroom Classic, because it isn’t stored locally. 

If you save a Photoshop document as a cloud document, there are at least two ways to get Lightroom Classic to see it again.

Method 1: Save a copy of the Photoshop cloud document as a local document again. It sounds like you tried this. However, if you had previously cataloged it in Lightroom Classic before saving a copy as a cloud document, Lightroom Classic is looking for the pre-cloud version in the folder it was in, under the same filename. So if you want Lightroom Classic to see it again, save it back to the same folder with the same filename it had before. (If you want to preserve the old local version, archive a copy of it before you replace it with the new local copy of the cloud document.)

Method 2. If you want the Photoshop cloud document to be cataloged while preserving its former local version, for example, if you want to see both of them in the catalog, then you’ll have to import the new local copy of the cloud document as a separate new item, not replacing the old one. So you probably want to make sure the new local copy has a different filename, especially if you want to store and catalog it in the same folder as its older version.

Yes, this is definitely a complication when you want to use the iPad apps on images cataloged with Lightroom Classic, and it is not fully resolved at this time.

I do not know if your workflow is "normal", but I would suggest you try this workflow to compare. I think you will find it easier.

1) In your LrC catalog, select a photo,

2)  [Edit in Ps ] or  [Ctrl+E] 

3)  [Save] the Ps image  (Or [Close] and [Save] )-  Not to the Cloud!  Not a [Save As]!  The Ps image (as TIF or PSD) returns to the LrC catalog.

4) Add the Ps image to a Standard Collection that is marked to sync to Lightroom (Cloud).

Now the Ps image that returns to LrC will be synced to the Cloud where it can be edited in Lr (iPad, iPhone ) and any edits done in mobile versions of Lightroom will automatically sync back to the Ps image in the LrC catalog & its Collection.

If you sync the source file in a collection before you edit it in Ps, you will have both the LrC source and derivative Ps image files in the synced Collection.

There are disadvantages to this method, that is- The sync of the image LrC to Lr is only a proxy (smart preview) with limitations, including not being a full-size file editable in iPad-Photoshop. It is limited to 2560pixels long edge.