Mounted filesytems should be visible to the mount command, and you can use that to test for the existence of the mount before running rsync:
mount | awk '{if ($3 == "/path/to/mount") { exit 0}} ENDFILE {exit -1}' && rsync ...
mount runs the mount command, which will display any mounted filesystems. That output is then piped (|) through to awk which looks for the third ($3) argument to be equal to the path you're looking for (/path/to/mount in this example). If the path matches then the command returns success (exit 0) otherwise it'll exit with failure (exit -1). The && will require that the mount command returns successfully before executing the part after. Any other return code is considered a failure, so exit 10, for example, would also be interpreted as a failure.