My undergrad degree was in Electrical Engineering. The methodologies learned in engineering definitely helped, but the specifics related to this field was obviously lacking. Without some luck I don't think you can make the jump with just the degree. Since your degree is rather technical, many will accept that as a degree in the field, but in my experience EE is a bit too low level. However, it would be fantastic for some hardware hacking and the like and you could leverage it that way.

If you show some prowess and passion in the area then that definitely supercedes any degrees.