Well as it turns out: yes way, at least according to Oskar.
The man's name is Joseph Koljaiczek, Oskar's grandfather, and according to family lore, Joe got Anna pregnant while he was hiding under her skirts.
The child turned out to be Oskar's mother, Agnes. Oskar's mother denies that this was how she was actually conceived, but Oskar tends to believe the story.
But back to the story…
Once the cops are gone, Anna and Joe are inseparable. They marry.
But there's a problem: Joe's on the run because he's a convicted arsonist.
So he takes the identity of a drowned raft pilot. All he needs is a few forged documents and voila—he's now Joseph Wranka.
Things go pretty well for a few years. But eventually, Joe (Wranka) runs into an old boss of his, who half-recognizes him as the guy who burned down his factory after an argument.
Eventually, the police start sniffing around and close in on the impostor.
One day, while Joe's piloting his raft, he sees police along the riverbank and dives into the river.
Joe swims underneath a giant raft made of logs, never, as they say, to be seen again.
According to Oskar (who's still telling us this from the asylum), there are several versions of how his grandfather's story ends.
In some versions, he finds a hole in the raft and is able to breathe until the cops leave.
In another, he escapes to America and makes a fortune for himself under the name Joe Colchic. Oskar thinks all of this is hogwash, though. He feels pretty confident that Joe died under the raft, though he jokingly mentions him again later in the novel as his rich grandfather Joe Colchic.