AFAIK no, that person would have to open each issue they want to approve (e.g. in a new tab) so they can edit it in JIRA. They can see the change they made only after Confluence has synched its JIRA issues macro.
What Confluence offers is overviews, graphs, lists etc of JIRA issues; these get synched once per hour by default IIRC.
In order to change an issue's status or description text, you can't just click somewhere in Confluence, but will have to open the ticket in JIRA and make the change there (e.g, transition to an Approved status, or check an Approved checkbox).
... at least as far as I know. Maybe you can find something helpful here:
https://confluence.atlassian.com/doc/jira-issues-macro-139380.html
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