There's nothing particular to worry about. With Dropbox, the key issue for LR is opening the same catalogue on more than one computer.
I would keep the catalogue and its preview away from selective sync, and just use it for the master files. Smart previews would allow you to work without downloading the masters.
You cannot store the Catalog "on" Dropbox: it must be stored in a normal local folder (computer attached storage of some kind). Only, Dropbox happens to be watching, and syncing to and fro as necessary, the contents of this local folder (against those of its cloud based counterpart for this folder).
A problem could arise if Dropbox was part way through copying your Catalog in or out, when the plug was pulled - which might leave you without an operable Catalog in the local folder. Or, if LR attempted to access this Catalog at a moment when Dropbox also had it in use, so as to replicate that across the internet.
If you are only using one PC with the Dropbox account then the local folder will always be where fresh change arises; hence all normal syncing will go outward from your local PC to the cloud (except in the case of disaster recovery). Provided you always give Dropbox a chance to finish what it's doing, and give LR a chance to finish what it's doing, that should all work smoothly for the image folders and for the Catalog. I'd advise suppressing the previews and smart previews folders from being synced though, which I think you'd need to do within the cloud Dropbox interface IIRC.
More robustly, you could maintain your Catalog outside of the Dropbox watched local folder, and target just your LR Catalog backups to happen inside the Dropbox watched area - so that it's those (and not your live working Catalog or its previews) which will get synced to cloud.
You can make frequent Catalog backups, at chosen discrete moments - cleaning out older ones periodically so that not too many accumulate, In this case LR is likely never in active conflict with the Dropbox utility - except as to external data, which can therefore be gracefully handled.