Probably. They then promptly watch those couple thousand troops drown when the Royal Navy sinks their transport. And if, by some miracle, they reach Iceland intact, they then get to watch them starve/die in battle as they have absolutely no way to resupply or reinforce them.
Absolutely conceded.
Even if "a couple thousand" troops can conquer Iceland, I don't see how they could hold it.
And a large portion of the naval ships that assisted with the invasion of Norway won't be available for the attack on Iceland on account of being underwater and/or awaiting repairs.
Well, my notion was that they invade Iceland instead of Norway.
Ah, forget it. It's a dumb non-starter of an idea and not worth debating. I admit it.