No, the group picker simply lists groups.
I've written fields that do that, for version 3 of JIRA, so I wouldn't try to use the addons in more recent versions. But they weren't hard, so I'd have a look in the marketplace to see if someone has done an add-on that you could use for it. I believe you could also use the Behaviours functions in the Script Runner add-on to change the behaviour of a standard group-picker.
I have multiple projects that use variations of the same base workflow. The variations depend on the requirements of the project or issue type. The variations mostly come in the form of new statuses ...
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