I don't have a consistent connection and ping gets high on occasion. Can I still play Portal 2 coop, relying only on the saves in between levels or do I still have to be online 100% during the whole game?
In my experience, the co-op level stops and immediately kicks you both out of the game if one person disconnects. I played on the Xbox 360 version, but I've been told the PC version exhibits the same behavior.
In my experience, there are generally at least one or two parts of each puzzle or puzzle sequence where timing is important. The game even gives you a way to give your partner a countdown in order to synchronize your actions with the other person. Trying to play on a very high latency or intermittent connection would likely be quite frustrating, but potentially doable if you're both patient.
Levels are in general short and your progress are saved automatically after each completed one.
I suggest you to let your buddy host the game, if he/she has a more stable connection and in general I believe you can enjoy the co-op part of the game without major problems, even with your inconsistent connection.