I would say the relays will stay latched to whatever their state was when signal goes (they would not be checking for signal status).
I can't see that much value in having a remote system that would only work when you are there though?
It would be a bit like a gadget I tried that allowed me to turn the awning lights on and off with an Alexa command - kind of fun in a "look what I can do" way but it was a bit of a faff to setup each time when a simplier system would do the job better as there was no need for unattended turning on of the lights
How about a Cerbo or late Venus GX running Node-Red? That would give control from any device, it could also check for internet connectivity and if none carry out certain rules.