I am often asked by readers if networking will really help them obtain a consulting interview or if it could affect them negatively.
My response is networking, if done properly, is never taken as a negative.
I suggest you network with anyone within a management consulting firm regardless of whether they are involved in recruiting or consulting resume screening.
Your goal is not to contact people who can help you in recruiting.
Your goal is to contact people in the firm for an informational interview.... which is basically, "Can I call you or meet you for coffee to learn more about your career path, whether you like working at XYZ firm, how you decided to pick this firm, what's it's really like day-to-day, whether the people are as nice as they seem," etc...
An informational interview is an interview where you interview them.
Then in your cover letter, you tell the reader how much networking you've done, who you have met, what you have discovered and why you like the firm (be specific).... and because you were so specific and you spent so much time learning about the firm, when you say you like the firm for XYZ reason, they actually believe you.
This is the first benefit of networking.... and this value is guaranteed in the sense that if you network enough and do what I indicated above, it will make your cover letter stand out.
As someone who has reviewed thousands of cover letters and resumes (which by the way is a very, very, very, very painful process because every cover letter seems the same... some mail merge, copy/paste cover letter that shows absolutely no interest, and no research into the hiring firm), a great cover letter + a good enoughresume will get you the interview every single time.
The second potential benefit is not guaranteed (at least not in a short time period). If you network enough, at some point, someone in the process decides to help you out in some unpredictable way - they introduce you to someone else, they get you an interview, they help your resume get noticed, etc...
It is very difficult to determine in advanced who is most likely to help you or how they will help you. Very hard to predict. You just do a lot of it knowing that at some point in the process, you will get some help from someone in some useful way.
For other suggestions on networking, consider my guide on How to Network to Get a Consulting Interview, for a specific process you can start using right away towards securing an interview.