Indeed the use of double quotes around "$FLAG" prevents the expansion of the wildcard. They can be left out, but then the test will fail if there are more files present with this pattern. To test for the presence of one of more files you could try:

Code:

FLAG=/test/Marker_*.tmp

file_exists() {
  for _i do
    [ -f "$_i" ] && break
  done
}

if file_exists $FLAG
then
  echo "One or more marker files exist"
else
  echo "No marker files have arrived yet"
fi

---
That should not be necessary, since wildcards are not expanded in variable assignments...