No, adding more points of failure doesn't make the first potential point of failure more fail-proof, or anything like that.

If adding a new layer (gmail) creates a new point of failure without creating any new resilience against failure, you're putting yourself into a bad position.

Think about failure like resistance. Points of failure in parallel gives less overall risk of failure. Points of failure in serial (like adding a front-end) gives greater overall risk of failure.

"Single point of failure" means a point at which a failure effectively breaks the entire system or workflow. A system may have many SPOFs, which is worse than a single SPOF, which is, in turn, worse than no SPOFs (that is, the desired case is no single failure kills forward progress).