Yes.
Rotom will ask you random questions throughout the game- but that doesn't mean that's the only way to activate Roto Loto. Tapping Rotom on an area that isn't the map will give you a heart sometimes, and this heart may cue a Roto Loto, and when evolving Pokémon, Rotom may cue a picture to be taken. So, even post-game, you can use the Roto Loto! I've also had Rotom ask me questions even after defeating Rainbow Rocket. (But the questions aren't about in-game events, they're more "Whats your favorite time of day?" etc.,)
Source: Experience In-Game