The tracks would need to be sunk further through the Southwest Corridor as the catenary infrastructure is not fully below ground level. Of course once you get past Forest Hills the tracks are not below ground whatsoever. Costs would be astronomical and the train traffic disruptions would be massive, for little gain.
As much as I would like to see this, I doubt we will ever see this in our lifetime. They blew a golden opportunity to do this while the big dig was under construction, and now costs to do this would be even more astronomical. That being said, I was looking at an MBTA document called Focus40, which itself is worthy of its own thread on there. The document talks about projects that the MBTA wants to do long term. Included in that would be a return of the Orange Line to Everett, an Orange Line extension to Roslindale or West Roxbury, the long awaited Blue-Red line connection at Charles, Electrification of the entire Commuter Rail system, and an E branch extension to Hyde Square among others.
You know what was not included in this document? The North-South rail link. This tells me that the MBTA has put the project to the back burner and its not a priority going forward.
I am going to start a separate threat about the Focus40 document, but for this thread, the takeaway from this document is no north-south rail link in our lifetime.