Eu estenderei seu script "launch":
#!/bin/sh
url="http://URL/"
online() {
wget -q -O /dev/null --timeout=5 "$url"
}
# infinite loop
while :; do
# launch chrome when we go online
until online; do sleep 5; done
google-chrome --start-fullscreen --incognito "$url" &
# kill chrome when we go offline
while online; do sleep 5; done
pkill chrome
done