That's very possible. It's very easy to forget try...catch and wind up with uncaught exceptions.
Honestly though, I would prefer the uncaught exception case. When an uncaught exception is thrown, it's very clear you have an uncaught exception and you know exactly where it came from. In the examples I wrote, you will accidentally catch an error silently. You will never know if anything went wrong unless silently catching the error triggers an issue somewhere else. Even then, it's pretty hard to trace back the bug to the lack of error handling code somewhere else.