Yes, the systems really don't care if the other one is running a totally different database.
You do want them separated and running in different areas though. The mysql install I've got here has one area for Jira and one for Confluence. Only one SQL service running, and if I need to dig through the data, I log in and then have to use "use jira" or "use confluence" to swap between them.
The only time you might struggle is if you rig up Confluence to read Jira's database for its users. You'll need to install two database drivers - one to read the Confluence database, and one to read the Jira. Just a case of being careful with the config though - once you get it running, it'll be fine.
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