Is it possible to connect a Sales Cloud org with multiple divisions to different business units using the marketing cloud connector?
If you are having multiple business units and have to connect to only one Salesforce org, you should be able to do it. In this case, the Salesforce org and data will always be connected to the primary business unit. Other business units however cannot reference Salesforce data directly.
If you enable the Multi-Org feature, each business unit can be connected to a separate Salesforce org. With the Multi-Org feature, I don't think there is a way to connect same Salesforce org to multiple business units. The connection might work in Marketing Cloud but not in Salesforce as you would face issues in fetching the tracking data in Salesforce from multiple business units.