Laurent,
If the DHCP server gives out an address and gateway information along with DNS you should be able to get Internet access.
The Node-RED flow will be started automatically after the reboot. One thing to note is that Node-RED is a little slow coming up on the Conduit so it may not respond right away. This is due to the limited resources on the Conduit.
You should be able to access the Web UI on the address that the Conduit gets from DHCP. One way to determine this is to log in to the debug/device console on the Conduit, execute an ifconfig command, and look at what address is assigned to the eth0 interface.
Jeff