Just reduce the NR yourself on the comment lines:
awk '/^[[:space:]]*#/ { NR-- } {sum+=$3} END { ... }' coriolis_data
Ok, this is the answer to the question you asked, but the question you really had in mind:
awk '{ if ($0 ~ /^[[:space:]]*#/) {NR--} else {sum+=$3} END { ... }' coriolis_data
(This is more awk-ish for using templates outside of blocks, as in the first answer, but for this you will have to write a comment template twice.)
: /.../ {NR--; next}, if-else. , , , - . !