How to Create Web Application in Drupal
Yes, you can build that type of data model using fieldable entities in Drupal 7.

For example add base "Member" fields to the user entity and use entityreference for the related reference fields on other entities (similar to a foreign key relationship)

The addressfield module provides a good standard address field and associated data structure to hold that info.

In your model, because it appears a "Member" may have many "Member Contact" records, you could perhaps just create a node type for "Member Contact" and add an entity reference field to the relevant "Member".

More info on Drupal 7 Entity API

Lastly, if you want to do it completely custom, you can define your own entity types with hook_entity_info