Harry Harrison covered this idea in “A Transatlantic Tunnel, Hurrah!” [1], which only had to compete with coal powered flying boats and nuclear trains.

[1] https://en.wikipedia.org/wiki/Tunnel_Through_the_Deeps

At it's deepest point it's about 8.5km down, for every 10 m of depth you add one atmosphere of pressure ...

It would probably make more sense to go overland in the opposite direction, through Russia, Alaska and Canada.