Chromecast will not work without an active Internet connection. For screen mirroring for your tablet it can work without one BUT it does need a router 'in the middle' (AKA both casting device and Chromecast need to be on the same WiFi as WiFi Direct, although announced at some point, was never implemented).
My bad, it seems that Guest Mode a few updates ago does allow this! I'll have to test it out as I'm not sure if this only applies to mirroring since streaming still needs an Internet connection and the whole point of the Chromecast is to let it stream instead of the casting device.