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In my personal experience, no. I rehabbed 1 of my student loans with Navient as well and when I look at my reports, it only shows good payment history from when I started the rehab. I'm actually surprised because I KNOW I missed some payments with them at first, but it shows "no data" for those 2 months and I have no late payments from it.
Wait... actually the age of the account DOES transfer over! Navient is listed as my oldest account (2006 - 12 years, 5 months) and I only rehabbed it a few years ago. However, I can only see payment history from the past 2 years, so I assumed the payment history wasn't affected.