No. PrimeGrid's servers work completely independently of Seventeen or Bust's servers. All coordination between the projects is done on a purely human level between the admins, not electronically.
Both servers have different lists of candidates they're testing, so we don't duplicate the same work. But we're both working on solving the Sierpinski problem. At the moment we're sending out work for k=10223 and k=67607 with 31M<n<32M.