Moving the entity to a new parent is fine and the base level data will move with the "C" entity. It will deconsolidate history, which will require you to reconsolidate prior periods. This will obviously change your financial results at the levels involved, but the data at the top should be the same. I'd tie it out when finished and test in dev.
You don't need to reload numbers for prior periods. A re-consolidation is enough.
In this regards, you might want to check the OrgByPeriod settings to keep history intact. However, this needs special attention to other related settings, so if it is not a requirement, just moving the member should be fine.