SSO relies on a common directory of users. Cloud systems have their own internal system which you can't connect up to other servers. So I'm afraid the answer is "no".
You might be able to code something that can take the Cloud authentication tokens and duplicates the process for logins for other systems, but I don't think it would be easy, and I've a nagging doubt that it would be very insecure, as well as add a "duplicate all users in two systems" overhead.
If you spend enough time as a Jira admin - whether you are managing a single, mid-sized instance, a large enterprise one or juggling multiple instances at once - you will eventually find yourself in ...
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