The west side connection will be severed, and all trains will be serviced out of Livonia Yard via the Lexington line. I'm not sure if that will remain the case once they switch over to R188s, which will be needed if and when CBTC get implemented.
You have no idea what a pain it has been to transfer shuttle trains off the west side connector from track 4. Due to the foot bridge that goes over the track, multiple departments must be present to take it down and put it back up, and the TA can't wait to be rid of that chore. Even a transfer off of track 3 is complicated, due to having to relocate the track 1 train to Times Square and using the hand throw switches, which means it can only be done between 0000-0500.
I neglected to mention in my last post that the main reason this project is happening is because the current Times Square platform is a disaster. It is not ADA compliant, it uses gap fillers (and once those act up, there goes service), and it can be confusing for the customers which train to board, particularly when track 4 is in service, where all foot traffic must go through a narrow area. The new platform will solve all of these problems.