I have no experience backing up to dropbox or iCloud; from what I remember it is not recommended to copy the DT databases to any location whilst in use. Copying the databases to a backup location whilst the database is closed would not be problematic.
You might want to look at Arq. It isn’t specifically advocated by DT, but is used by the company president (source: Heads up when using Arq to backup Devonthink). There appears to be no problem backing up open databases. Arq will backup to a cloud provider you specify (not iCloud as far as I can tell, but Dropbox; if you use Office 365 you might also have a terabyte of Onedrive space, which could also be used). It is a one-off purchase if you don’t use Arq’s cloud service). (I am not affiliated, and I’ll point out that on going from v5 to v6 Arq caused some of their user base quite a headache; their format is proprietary, which is not what I want from a backup, but looking into all this I found it to be the solution which best fit my needs)