Hi there,
no, a child content template has to use the Parent display rules and you would set the Apply to option. Which can be:
First post
Post with Term
Post with Custom Field
The way you use it is to
1. set the Parent content template rules eg. All Archives.
2. create child content template(s) and set an Apply to option eg. Posts with Term > Category > a term
3. repeat #2 for as many children as you require.
In this example you you can set a single Content Template to be displayed on All Archives and then overwrite them using Child templates that have specific conditions.