Yes! Although I did not find any documentation for it, and therefore it may not be a stable solution. I found this using browser developer tools. Make sure that the "Only when manually confirming" checkbox is selected.
Here is an example:
curl 'https://jenkins/job/z-promotion-test/3/promotion/promotionProcess/promotion_test/promotionCondition/hudson.plugins.promoted_builds.conditions.ManualCondition/approve' --data 'json=%7B%7D&Submit=Approve'
Authenticated version
curl 'http://<user>:<token>@jenkins/job/z-promotion-test/3/promotion/promotionProcess/promotion_test/promotionCondition/hudson.plugins.promoted_builds.conditions.ManualCondition/approve' --data 'json=%7B%7D&Submit=Approve'
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