Welcome ELM,
Yeah, get away from a 777 simulation, and stop thinking about deicing - think don't fly an iced plane, nor a plane in ice - at all... and you'll be better off for your initial flying. You'll be trained for icing when you need to be.
There is a lot to know and understand about flying a light airplane, much of which has little commonality with a 777 - don't learn about jets until you need to, when you need to, learn then, you'll be ready. If you try to carry backward big airplane systems and handling knowledge to primary flight training, you're going to certainly defeat your own efforts, and really annoy you instructor. If you're defeating your own efforts with misplaced knowledge, and annoying your instructor, there are two certain results: It'll take longer, and cost you more money. If I were you, I would not mention jet flying at all - for years. I speak as a 45 year pilot, with 85 types in my logbook, not one of which was a jet!
If simming helps you with navigation, airspace and radio work, okay, with caution. But handling should be learned under the direct supervision of an instructor, in a real plane.