until is the opposite of while. It’s nothing to do with doing stuff while another command runs. For that you need to run your task in the background with &.
cp SOURCE DEST &
pid=$!
# If this script is killed, kill the `cp'.
trap "kill $pid 2> /dev/null" EXIT
# While copy is running...
while kill -0 $pid 2> /dev/null; do
# Do stuff
...
sleep 1
done
# Disable the trap on a normal exit.
trap - EXIT
kill -0 checks if a process is running. Note that it doesn’t actually signal the process and kill it, as the name might suggest. Not with signal 0, at least.