Can cloud connector synchronize my multiple bigcommerce store's data to a single Zoho CRM,

Can cloud connector synchronize my multiple bigcommerce store's data to a single Zoho CRM, Salesforce, HubSpot, etc?

Yes.
The Cloud connector app can synchronize your multiple store's data to a single instance. 
The app assumes that every store is different and every instance (Zoho CRM, Salesforce, HubSpot, etc) is different, So it connects multiple stores data.