Yes, you can. And here's how.
My name is Travis Combs. I started in July, 2007 as a complete beginner. I had no previous musical training. I could not read music, and did not know that I had a musical ability. Now I can read and write sheet music fluently, I can set up and tune my pipes well, and qualify as a competitive Grade 2 player.
There is no need to start with an expensive set of pipes. Rather, your first instrument is what is known as a practice chanter. This is a single tube instrument shaped rather like a clarinet or a tin whistle. It allows you to learn the techniques without a large investment. A plastic practice chanter can be had for $50 to $100. Typically, you will practice with this for about a year before going to the next step. By this time you have proven that you will be able to play the bagpipes.