Learn English – Could “Hats off!” be insulting in some situations

Yes, "Hats off!" can be used in the insulting sense in several situations.

Before we get to the examples of such situations, here's a brief history on the origin of the phrase "Hats off!" from this wiki.answers link

While most American men no longer wear hats (except in cold weather or as a fashion statement), there was a time when the hat was part of the business uniform, or identified you as a member of upper-class society. In England, men wore top hats (also called stovepipe hats) when dressed formally, as did Americans, in the 1800s and early 1900s. The style of the hat gradually changed (stetson hats became very popular in the American West); but the custom of briefly taking off the hat was historically a sign of respect, whether for one's boss or for someone in society who was superior in status. In centuries past, taking off the hat might be accompanied by a slight bow of the head. Taking off the hat was also considered to be good manners for a man to do whenever a woman entered the room. (In western movies, the cowboy would always tip his hat to a lady.) Expressions like "hat's off to you" or "I tip my hat to you" thus became ways of showing admiration. And even though most men no longer wear a top hat, the expression has lived on. A version of it also survives in baseball: players from one team may say they tip their cap to an opposing player: for example, Team X loses to team Y in a very close but well-played game. The pitcher from Team X tells reporters, "I'm sorry we lost but I tip my cap to their pitcher. He pitched better than me today." So, to sum up, the expression goes back to the time when the hat was an essential part of a man's wardrobe, and taking it off or touching the brim were acts that showed admiration or respect.

The FreeDictonary.com defines "hats off to somebody" as-

hats off to somebody- something that you say when you want to express your admiration for someone

An Example-

Hats off to her - it takes a lot of courage to go travelling on your own at that age.

So, like Jim mentioned in his comment, you can take any interjection(or any expression conveying emotion) and use it in the negative sense. Here are some examples of the usage of "hats off!" you're looking for-

Fed up with the incompetent customer care representatives, Jim shouted-"You wasted an hour of my time just for nothing!!! Hats Off to you guys" and banged the receiver.

and

Disappointed with the class performance at the year end, the old professor just stared blankly at his students and said- "Wow, Hats Off to you guys."