They've been connected since 1991[1]. Amtrak runs trains from Canada/Chicago/Vermont into Penn using this connection. Trains run down Metro North's Hudson Line, through a junction in Spuyten Duyvil[2], down the West Side Line[3] (former northern section of the High Line[4]), and into Penn through a tunnel under the LIRR's West Side Yard[5]. You can see the connection here[6] (follow "EC Freedom Tunnel"). The connection under the West Side Yard was built in '86. The rest of the tracks are over 100 years old.
[1] https://en.wikipedia.org/wiki/West_Side_Line#Empire_Connecti...
[2] https://goo.gl/maps/DgeeiQzryseFg6A5A
[3] https://en.wikipedia.org/wiki/West_Side_Line
[4] https://en.wikipedia.org/wiki/High_Line
[5] https://en.wikipedia.org/wiki/West_Side_Yard
[6] https://www.openrailwaymap.org/?style=standard&lat=40.756798...