https://www.gnu.org/software/parallel/man.html#EXAMPLE:-Using-shell-variables says:
parallel echo ::: "${V[@]}"
You do not want the echo, so:
parallel ::: "${cmds[@]}"
If you do not need $cmds for anything else, then use 'sem' (which is an alias for parallel --semaphore) https://www.gnu.org/software/parallel/man.html#EXAMPLE:-Working-as-mutex-and-counting-semaphore
while [[ <condition> ]]; do
if [[ -s $cur_archive_path/log.${doy_ctr} ]]; then
sem -j+0 <cmd_to_run>
fi
done
sem --wait
You have not described what <condition> might be. If you are simply doing a something like a for-loop you could replace the whole script with:
parallel 'if [ -s {} ] ; then cmd_to_run {}; fi' ::: $cur_archive_path/log.{1..3660}
(based on https://www.gnu.org/software/parallel/man.html#EXAMPLE:-Composed-commands).