Checkin approval process does not tie into Branched rulesets, however starting in 7.3, there is a Branch Review feature that has been implemented. There are flags that can be set such that if the branches are unreviewed then merges are not allowed on the branch. This should provide a similar workflow to the checkin approval.
When using Branch based development pattern, the individual checkins have been emphasized less, as it is likely the review needs to happen on the entire change set that will be in the branch. Best practices for branch based development would include
Ensure that branches are short lived, it should only be associated with the story of bug, merge as soon as that work is done and reviewed
Ensure that the changes introduced in the branch are off high quality, leveraging the branch quality landing page
Review the entire change done in the branch - using the branch review feature
Given this workflow, the rule checkin approval is not as relevant as we see it.