Should all Analysis Units after migration have dependencies to Database objects?

No it's not mandatory. In CMS, we provide some default technology -> technology dependencies. When you start to define a precise dependency between elements of these technologies, the default is deactivated.

You've 2 use cases for dependencies:

  •  A discovered dependency : it comes from the DMT and it concerns only intra-technology.
  • A user defined dependency : it is created by the AIA inside CMS or by the upgrade process

Please also check CMS - CAST Management Studio for a detailed explanation