Would a triplane be way more efficient if the wings intersected at the tips to create one wing tip vortex instead of 3?
Well, those nasty wing tip vortices really can't be helped if you are creating lift.  Amazing that airliner designers in this century are still considering biplane vs strutted mono plane vs cantilever mono plane concepts in their proposals.

Bringing 3 wing tips together will create all kinds of air flow issues (remember to model at all possible AOAs), reducing efficiency.

The most efficient way to create lift remains a high aspect mono wing.  I would look to designers actually reducing sweep a little (around 15 degrees for subsonic) and try for as high an aspect wing as possible, just like sailplanes.

However, wing span constraints and support benefits for very large aircraft may yet see the return of the biplane, with very thin, high AR wings.  These could be swept a bit more at the tips, and/or endcapped or wrapped.  Fuel and landing gear could go in a more drag efficient longer fuselage.  Note mounting them in "classic" Tiger Moth style retains the stability benefits of wing sweep, which may be lost in the newer "Prandtl wraparound" proposal.

It seems some designers just can't bring themselves to make a 21st century high AR Jenny.  It might be worth a try.