Yes, I believe the purpose of the green line is to relieve any pressure in the red signal line to the actuator when the boost signal is removed. It's the "dump" from the litte black valve with the electric plug on it and a number of red and green tubes coming off of it. It is going to the compressor inlet side of things, so it sees no pressure, and you wouldn't necessarily want a portion of your intake system open to the atomosphere unfiltered so they ran it back into the intake track pre-turbo.
FWIW, mine has been laying in the bottom of my valley plugged in for quite a few years now with a plug in the nipple on the intake tube.
It is OEM equipment. It's not anything new by TN or by Garrett. Just stick that little green plastic hardline in there a good ways and it should stay put just fine.