Are my chances ruined?

I recently decided to pursue a career in investment banking and one of the most important is networking, so I started to reach out to alumni from my school. I probably sent out 50 emails so far. The problem is that I sent out emails to multiple people (around 2 analysts and 2 associates) in the same firm in the same city either on the same day or within the span of a few days and burned through pretty much every alum at these firms. I recently heard that emailing a bunch of people in the same firm can get you blacklisted. So have I ruined my chances of creating a network and eventually getting a job at these places?