Value of knowing a VP or other exec at a top tier PE firm

I am going into my final year of undergraduate studies ( Finance BBA) at a non-target university. I have done extensive networking and have developed solid relationships with several respected players in the PE industry. How useful will these relationships be for me in terms of landing an interview and a job, despite coming out of a non-target and with only two summers worth of internships? I am curious how far a good relationship with a VP/Exec could get you in the recruitment process. Any help is appreciated.