Atlassian officially released guides how to set up Bitbucket Data Center on Azure so definitely it is possible (like on any other hosting platform). There is not a big difference in installing Atlassian Apps on Azure, AWS or Google Cloud.. You need a machine, database, proper network settings and basically that is it. Of course individual steps would be different but the idea is not.
If you want to read more about Bitbucket Data Center you can check this KB ..
and even use some templates..
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