Listing ORCiD in LaTeX papers
Several publishers (Wiley, Elsevier, Hindawi, more are listed here) allow you to attach your manuscript to your ORCID ID. Like other metadata, this ID is entered in a form at the submission stage, it is not part of the LaTeX code (which in most cases is converted to XML right away). The typical workflow is explained here.
If your manuscript is in MS Word, you can include the ORCID ID in the author list and the conversion to XML will pick it up (as explained here). I am not aware of a LaTeX implementation with the same functionality.
So I would say the answer to your first question is that form-based entry is presently the accepted way to tell a publisher about your ORCID ID, and the answer to your second question is "no".
I recently had a paper accepted where I included the ORCiD in the address field of the LaTeX code, as suggested in my comment to Carlo's answer. The publisher did not ask me for any form-based entry as part of the publication process.
The publisher (Springer) did automatically recognise the ORCiD identifier from this and included it in the metadata. IIRC the paper was automatically added to my ORCiD record by Crossref upon publication as a result.
This may not be representative of other publishers, but I do conclude that it is a good idea to include an ORCiD in the address field, and that there is evidence that this is picked up as part of the publication process.