@silas,
I am not completely sure what the exact question is, but I will try to resolve most of the implicit questions.
Backup and restore of mysql databases
Plesk Panel and/or any other common (sql/mysql) tool can be used to create (frequent) backups, that can be restored at will.
A restore of the database can be started in the case of storage, disk and/or server failure.
Mysql cluster
Clustering of mysql database servers is one way of allowing continuity of database presence, irregardless of the nature of the failure.
This solution requires at least two servers (and more is better), with associated costs therefore rising.
Moreover, the associated costs can become even higher when having to set-up and/or maintain the cluster infrastructure yourself.
Percona Cluster is a common open-source solution for mysql clustering, but that does not alleviate all of before mentioned costs.
Another option is to use ClearDB, in order to have a clustered mysql environment, set-up and maintained by the associated company.
However, even that is not a real solution, since databases outages can become costly or even prevent proper working of the database(s).
Mysql mirroring
In a sense, a simple alternative to mysql clustering is what I call "mysql mirroring".
This implies the creation of a very small server or VPS, running an identical mysql server and identical databases.
With some easy (my)sql scripting and/or even rsync, you can synchronize the databases/servers on a frequent basis.
Whenever the master mysql server is going down or encounters data damage, one can switch (manually) to the "mirrored" server.
Note: discrepancies between servers can exist, dependending on the frequency of "mirroring", hence implying that this approach should be viewed as a "dynamic backup".
The obvious advantage, in comparison to a static backup, is that the "mirrored" server can be started up faster, hence reducing downtime and problems thereof.
Also note: with some advanced scripting and usage of drbd, corosync, pacemaker (and similar) the "mirrored" server can become a continuous mirror, that is automatically enabled as the master mysql server, if a failure on the other mysql server occurs. This advanced scripting hence results in a full HA cluster.
The obvious advantage, in comparison to before mentioned full HA Cluster, is that a "mirrored" server approach is more easy and more cost-effective.
Conclusion
In general, it is good to have some kind of backup or mirror or cluster for mysql servers and associated databases.
The proper choice depends on your ability to maintain the solution chosen.
However, whatever the choice may be, Plesk is supporting any choice made, in the sense that Plesk
- can work with external mysql servers, hence not excluding (external) clusters (Percona Cluster for instance) and/or database solution providers (like ClearDB),
- supports various external mysql based servers, such as MariaDB, Percona (and with simple dbases, even MS SQL can be used)
- allows for backups of local database servers, with the possibility of scripting backups
- support that the native (local) mysql database server functions as a master of an external (slave) mysql server
and so on.
In short, the answer to your question is: yes, it is possible, in various ways.
However, the main question should be why to host databases and/or Plesk on a server that breaks down and/or can break down in the future.
In a sense, you want to create a solution for the case that the current server breaks down (again) and you are potentially willing to make costs to create a solution that entails both the current server and a new server (the failover server), while migrating to a new, good and solid server would probably prevent costs of a failover server.
It is my advise to reconsider your current hosting server, instead of emphasizing the desire to have a backup or cluster solution.
After all, without the faulty (current) server, the desire for a backup or cluster solution would be less prominent.
Kind regards....