As perfinit said: Relax!
Yes, TCAS is "efficient," even outside of primary radar coverage.
There are other means to establish position of oceanic aircraft. Generally, aircraft at the same altitude will not be within 60 or 30 miles of each other.
You can "What if???" this to death. In 2015, 560 people died in airline accidents, and two of those were deliberate (bomb; suicide).
Meanwhile: 1.24 MILLION people die worldwide EACH YEAR in auto accidents. 24,000 people die worldwide from lightning.
17.3 million people die each year from heart attacks.
You should probably worry more about your drive to and from the airport, the food you eat on the plane, and spending time on the beach in California under a "little rain cloud" than about your flight getting there.
Relax.