Does Multiversion module need content migration if enabled on running site?
As mentioned in the Multiversion description on Drupal.org that it should be enabled on the fresh instance of the drupal. If you are planning to use multiversion on already established database then on enabling this module it will erase all the entities including the custom ones. It will delete
all Taxonomy Terms, Menu Items, Content, Config Entities. So that will require content migration on after install. But there is another way, 
1. Install a fresh database
2. Enable the Multiversion
3. Sync the configuration.
Configration management comes really handy in this case.