Surgical techs have their own specialty and education. While many programs may offer an associate's degree, the education is very unlike nursing. Also, keep in mind that most places will pay much less for a surgical tech than for a nurse. STs have a salary cap right around where RNs start where I work. Also, an RN will have much more flexibility as they can move to different units, while STs are pretty much OR or maybe L&D for c-sections.
Ways to get your foot in the door include working as a pt care assistant in the OR. It's not a glamorous job and doesn't always include a lot of pt contact, but it will help you make contacts and networks within the OR. You can also look at joining AORN as a student nurse and networking there as well.