I don’t know what synergism is to answer if Catholics are, but what I do know is what you ought to tell your Calvanist friend.
There’s a problem with your Calvanist friends’ assertion. The analogy has clear corresponding points to reality. The guy on the boat directly represents God. The guy in the water directly represents us. Now, if the guy in the water is dead, he is beyond the help of the guy on the boat. The guy on the boat can’t bring him back to life. Now they may say that God can do that, but it breaks the analogy because the guy represents God but he is not really God.
The point is that in our lives, are we ever beyond God’s help? Of course not. So the guy in the water can never be beyond the help of the guy on the boat. The analogy is best explained this way:
The guy in the water is us in life surrounded by the water which represents sin. On our own, we can’t do anything about the water (sin) and it will eventually overcome us. Only the guy on the boat can bring us out of the water (sin.) The guy on the boat wants to save us, though. He throws us that life preserver and asks to hang on. If we do, he’ll pull us up. If we don’t, we are overcome by the water and then we drown and then we die and are beyond his help.
That’s where their point falters. If we were dead and drowned, we’d be in hell. That’s what drowing is in the analogy. I mean, a person doesn’t just hit the water and then they are drowned. Even if you can’t swim, it takes a few minutes. The guy in the water represents us in life. So if him dead is us in life, what does he represent before he drowns? Is there some state in life which we’re in when we’re not drowned in sin? Of course not that makes no sense, and I’d imagine the Calvanists would even more forcefully oppose that.
We also have to remember that Calvanists, or most of them, believe God is basically controlling everything we do. He is totally sovereign, so in this anaolgy the guy on the boat would have a big long stick and he’d be moving us around and making us do stuff in the water with it before he saved us. He’d also probably have to fly down next to us and take our cold, dead, stiff arms and wrap them around the life preserver for us before he flew back up and pulled us in.