I would say it's probably bad. It reminds me of some code I read that a coworker wrote a while ago - in a public helper method, instead of throwing an exception, they did a MessageBox.Show() with an error message. That was pretty bad for several reasons, one of those being that I wanted to use the method without showing a stupid error to the user.
Personally, I like to have control over whether a method logs information or not (for the most part). What if I want to handle the exception in a way that doesn't clutter my log files?
On the other hand, maybe the person who wrote the code designed it this way on purpose, to make sure other programmers didn't get away with NOT logging when they should. It depends on the scenario.
I personally don't like it because it's a separation of concerns problem - the logging should probably be decoupled from the task that the method is trying to perform. Unless logging is an essential part of that task. And for certain exceptions, the logging may very well be important.