Can I use copper tape to connect Live AC power?
Technically, yes. But you shouldn't. There are some drawbacks to this:


It won't be capable of the short circuit current, you'd have to alter the fuse rating.
It won't be properly insulated. 
Applied isolation can be easily punctured, since it isn't inside the wall or a tube.
It won't meet any electrical building code.


I suggest that you get a 12V isolated power supply and use LED lights.
It will be a safe voltage, a low (short circuit) current and still give be able to supply 10 Watts (1 Amp). 

You might need to check for the thickness of the copper tape before use. And check it is capable of the current that you will require.
I suggest that you look for flat speaker wire and use that instead of copper tape.