No, the filing will be sent to the error queue and not be allowed to process through. You will likely get a document transmission error. Many times the document will not be stamped due to the type of document to be stamped not being in the appropriate format.
That is the official answer from eFileManager. In practice, however, we occasionally see accepted filings with the lead document not containing a file mark. That is generally because the clerk had to manually process the filing and the file mark is not applied.
We can ask eFileManager to provide a file marked copy to you.