We don't recommend it. The Salesforce Integration User licence is designed for non-native tools, like Zapier-style workflows, where credentials are stored off-platform and a more limited licence makes sense.
Mailchimp for Salesforce is a native application. Credentials stay inside Salesforce, the integration only ever makes outbound callouts, and the sync user never grants access to an outside entity. Many of our screens and processes also run entirely within Salesforce, which an external tool wouldn't need.
For that reason we recommend running the sync under a System Administrator licence with our Admin permission set assigned. The permission sets ship with the package and are updated when you upgrade.
The Integration User licence also has practical limits. It is restricted around record assignment, and Salesforce doesn't let you log in as the integration user, so you can't set it up as the Sync User or Security Owner from General Settings. Workarounds exist, but they add complexity and aren't something we support.
Note: If you'd like records we create to be owned by someone other than the sync user, assign a Security Owner instead. That setting controls ownership of the Mailchimp members, contacts and leads the integration creates, independently of who runs the sync.
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