Yes you can crumb coat the cake the night before.
When you make the cake and then crumb coat the cake you should refrigerate the cake with the crumb coat.
You can let the crumb coated cake sit in the refrigerator for a few hours and then it will be ready or you can just leave the crumb coated cake in the refrigerator overnight.
So yes you can crumb coat a cake the night before you're ready to serve it.
You can make cakes a day or two in advance and have it ready to serve or eat when needed.
You can crumb coat a cake 2 days in advance so crumb coating the cake the night before is okay as well.