Assuming the database replication is invisible to JIRA, this can work. I've seen cases of Oracle RAC working with confluence for example. However, note this is not officially supported by Atlassian.
As Renato said, I would recommend to work with the database you are most proficient on.
Actually we don't have a specific documentation to Database replication. But you should be able to setup a master -> slave replications with no big issues. About what database you should use, my recommendation is you use a supported database and one your DBA feel comfortable to work .
However, if you are concerned about disaster recovery issues, I recommend you to have a look on the Data Center edition:
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