If I understand your question correctly, then the answer is no. Alfresco uses a database like MySQL to store the document metadata, which is then displayed along with a document in Share. You will not see anything about the database (schema, tables, etc) inside Share.
So, installing an additional database on your server/laptop will not have anything to do with Alfresco and will certainly not be visible within Share or any other Alfresco UI.
Hope that helps,
Digital Community Manager, Alfresco Software. Problem solved? Click Accept as Solution!