Thanks to the comment on this blog post (which, by the way, has a very useful DTF Custom Action example), I found the Wix EnsureTable element , which ensures that the table will be displayed even if it is empty.
, , :
<CustomTable Id="MyTable">
<Column Id="Id" Type="string" Category="Identifier" PrimaryKey="yes"/>
<Column Id="Root" Type="string"/>
<Column Id="Key" Type="string"/>
<Column Id="Name" Type="string"/>
</CustomTable>
<EnsureTable Id="MyTable"/>