How likely do people get a job interview through connections?

Limited Brands is offering positions for internships for next summer. I’ve been wanting to work for their company for so long and I seem to fit the requirements. I put in my resume just about a couple weeks ago but still haven’t heard from them.

My boyfriend’s sister works for the HR department and she’s been with them for about 5 years. I know she has some seniority but she’s not a director, manager, or anything like that. She knows how badly I want to work there but hasn’t put in a good word for me. We get along great though.

Should I ask her to try to put in a good word for me some how? I don’t know how she should do it or even to figure out who’s in charge of internships. I have a feeling that getting this job is kind of through who you know because it’s such a big company.