It depends on what type of RCD it is, the switch will stay on in some types of RCD, and others the switch will turn to off if there’s power loss, both will disconnect if there's a leakage to earth which can be caused by incorrect wiring or something such as a 'borrowed neutral', which is where the neutral from one circuit is used to supply another, potentially dangerous and will cause RCD's to trip out
This RCD in the kitchen, is it a plug-in RCD or one that’s hard wired, also what is wired after the RCD, just the bath or is there anything else?
Does the switch stay and then go off, or does it stay off all the time?
does it look like this?