Can I add copper wire led lights to existing 12V Landscape Light Transformer
If "some sort of an adapter" is a 5V voltage regulator which can accept 12V or more input, perhaps yes. If not, no, and more may be needed if either one is AC, not DC. 

You may (quite probably) also overload the 12V adapter if it's matched to the current string of lights such that adding more load would exceed its capacity.

Simpler and safer to just run the 5V adapter to a plug.