Would be best to understand the rules of binding and unbinding of templates works e.g. unbinding and retaining configuration as well as what can be overridden locally for each site.
Of course the consensus for deployments is generally making sure you have a testing process in place that suits you. E.g. Unbinding Site and retaining Config > Making adjustments > Monitoring Impact on-site > Accept/Reject > Consider impact on all affected sites > Make changes to Template and Bind Test Template back.
