I haven't watched Greenway much. My initial reaction is pleased though. Even after reading more about him and his advanced stats. We need defense from our forwards which he'll provide. Since we have three 2nds and a decent prospect pool now, giving up our 2nd-4th selection in the upcoming draft is worth it to get NHL minutes at a position where your best player just got hurt in the middle of a playoff race. He'll probably help more than nothing in a hockey sense, it shows management is taking initiative to try and make the team better when it counts, and the price we paid doesn't seem horrible.
If he's a black hole and actively makes the team worse, obviously it's a bad trade, but I have to trust management and pro scouting enough to give them a roll of the dice here.