Once again, quoting my favorite source when it comes to these sort of issues, per K. Demoff, the salary cap implications of signing draft picks is considered a separate entity in his approach.
He stated that the way it usually works out, given the way the salaries figure against the cap in the off season, (only the top 51 actually count), the $$$ used to sign the draft picks, are offset in the long run by merely replacing the players on the roster that don't make the final 53.
Hence, all this talk about "needing $6.1M" to sign the draft picks, out of the remaining salary cap $$$ is not entirely accurate.