Which thing? The DataCrystal mechanic? I've never used Itch's program, so I'm not sure. If it's like Steam, then in theory it should be the same: just hunt down the folder and swap stuff around. But I suppose it's possible it might put some kind of protection on the files to prevent "corruption" or whatever. I'd say give it a try, and if it doesn't work, fall back to just downloading.
But if by "app" you mean anything related to mobile, absolutely not. This game is very much PC only.