You can do that - I do it all the time myself - but I'd stop short of saying, "you'll be fine." That approach has its own downside, which is that it makes life obnoxious if you ever do want to actually handle exceptions. Then you'll have to add extra logic to determine if the exception you've caught is the actual error, or just a wrapper of some type. So your error handling inevitably becomes more error-prone.

If you can get your team to commit to a "let it crash" policy, though, then it's pretty doable.