You will get interviews based upon your credentials. From there, when you show up at interviews, the biglaw law firm may be suspicious of a non-trad student's willingness to work the long hours. Don't give them any reason to be suspicious of you - and then it is an even playing field. In fact, if you have a track record of working the long hours, it may give you a leg up - in that they know that you know what you are in for, lack of naivety working to your benefit.