Online-only files can't be backed up
Dropbox Professional offers a "Smart Sync" feature that allows the user to store files only in the cloud. What remains on your Mac is a 0-byte placeholder file. If you attempt to open the placeholder file, Dropbox automatically downloads the data of the file to your Mac and the document opens. While this is a convenient feature that allows you to free up some space on your Mac, this feature removes files from your local storage, which means that CCC can't make a backup of these online-only files. Before using the Smart Sync feature, you should consider whether you are comfortable with not having a local backup of the files that you choose to store only in the cloud.
Dropbox placeholder files are backed up as placeholder files
When you ask Dropbox to store a file only in the cloud, Dropbox deletes the local copy of the file and replaces it with a proprietary, 0-byte placeholder file. As noted above, when you open a placeholder file in the Finder, Dropbox downloads the original. Likewise, if you attempt to copy a placeholder file via the Finder from one volume to another, Dropbox downloads the data to the source, then copies the original file (leaving the downloaded source file in place). CCC backups do not behave like Finder copies. And for good reason – if you have 1TB of online-only files on your 500GB SSD, you wouldn't want Dropbox to download all of that data when CCC attempts to make a backup! Rather, CCC copies the placeholder files as they are, retaining all of the placeholder attributes of the source files. CCC makes a non-proprietary backup of your files; our goal is to make the destination files look exactly like the source files.
Dropbox's proprietary placeholder files are not transferrable from APFS to HFS+ formatted volumes
If your Dropbox folder is on an HFS+ formatted volume (the default filesystem up to macOS Sierra), Dropbox will flag an online-only placeholder as a compressed file. The file is not technically compressed, of course, because no data is stored locally. This clever hack works, but this is an unconventional use of the "is compressed" file flag. As far as backing up these files is concerned, though, the hack is fine – CCC will preserve these placeholder files when copying to another HFS+ volume, or even to an APFS volume.
If your Dropbox folder is on an APFS volume (the default filesystem starting in macOS High Sierra), then Dropbox creates a sparse placeholder file. A sparse file has a logical size that is larger than its physical size. In the case of a Dropbox placeholder file, the logical size would be the size of the real file (e.g. 2.4MB), and the physical size would be 0 bytes (because no data is stored locally). A sparse file is a much better device to use for creating a placeholder file insofar as it is non-proprietary, and this is likely why Dropbox chose to use sparse files in favor of the compressed file hack. However, not all filesystems support sparse files. CCC can only preserve these placeholder files when copying to another APFS volume. If you back up your APFS-hosted Dropbox folder to an HFS+ backup volume, the placeholder files will consume all of the space of the real file, but will contain no data (just a bunch of zeroes). While this is functionally consistent with the content of the source file (no data stored locally!), your backup will consume considerably more space than the source. This is not a limitation of CCC, this is simply a limitation of backing up APFS volumes to HFS+ volumes.
If you're using Dropbox's Smart Sync feature, we recommend excluding the Dropbox folder from your backup if your source volume is APFS formatted and the destination is not APFS formatted.