In 3 games Carrier will have played 40 games, making him eligible to meet the requirements for 1 of 2 forwards that must be exposed in the draft that are under contract and have either played 40 games in 2016-2017 or 70 games between 2015-2017.
Separate is the distinction of who is exempt from the expansion draft, which is any player currently playing in his 3rd or later professional season. Carrier is in season 3, so he is eligible for the expansion draft (Reinhart, Eichel, Bailey, Baptiste, Fasching...not)
The Sabres currently have 6 forwards that meet the forward requirements (O'Reilly, Okposo (NMC), Ennis, Kane, Moulson, Deslauriers) If the Sabres manage to trade Moulson and or Ennis, it would be good for Carrier to get his 3 games so that he could be exposed. That said, I fully expect Moulson, Ennis and Des to be exposed, so Carrier's games don't really matter. But they do give the Sabres flexibility.