Can the new TT cyborg can target through an object. Can he target through the batman cowl if it is worn by a character?

Are you asking if Cyborg sees through stealth?

He does not

By asking specifically about the Batman Cowl "if it is worn", he is asking if he could use an assigned relic for Cyborg to draw LOF.

If so, then answer is "no". Relics, when assigned to characters, are not held. They are not on the map at all. There is no way for Cyborg to interact with an assigned relic (or resource, if that was your next question).