There are different methods to achieve the same purpose to try to get multiple machines to connect to one remote MySQL server. What Ken has stated is sound on the option to keep Horde and simply change the password and re-sync it for all the machines. I personally believe it is easier to not use Horde at all and convert Roundcube to SQLite.
Next, please note that there is nothing in our documentation that states you cannot have multiple MySQL machines connected to a remote MySQL machine. This doesn't indicate we support that setup. If you want to pursue multiple machines to one MySQL machine, you can do it but you will run into some issues that I had already mentioned originally. For example, another consideration would be eximstats and cphulkd also have individual databases. eximstats is going to be skewed for users on both machines and cphulkd will probably need the password re-sync for it as well (if you are using cphulkd on the machines). If cphulkd blocks a user on one machine, that user is going to be blocked on the other machine(s).
The biggest issue beyond the webmail clients; however, is one I already noted that usernames cannot conflict. You would not be able to have a user admin on one machine and another user admin on another machine. If you do, both users will likely be able to see the databases of the other user in their cPanel account due to the wildcard grant for admin_ for cPanel systems with database prefixing, which looks similar to the following:
As such, you cannot have the same user on multiple machines in this setup.
GRANT ALL PRIVILEGES ON `username\_%`.* TO 'username'@'%'
Ken and I discussed this entire matter prior to my latest reply. As far as I can see, we are simply indicating different mechanisms to use for webmail in the setup you are wanting to try.
Finally, if you do end up trying to achieve this, please only setup two machines for testing it out initially to ensure it works and you are able to see what issues arise. This way you can easily convert back if needed.