Hrm. The number quoted doesn't sound interesting because it sounds fake. $1 billion dollars sounds like something Dr. Evil would say, not a real figure that got worked out in some SEC filing.
I like how you broke down the different categories for search revenue related to mobile though. Let's put some phony amounts on them just for fun.
Let's begin with the assumption that Google gets $1 per mobile search. (I'm using mobile search here because that's the category of search we are interested in.) That is, every mobile search, on average, generates $1 in revenue.
1) Mobile searches which were made on Android but where, if Android hadn't ever existed, the user would have had another mobile device and made the same search anyway.
Google loses money here because the search would have been made anyway. The loss comes from developing Android. Let's say Google loses 10 cents. (Total BS number!)
2) Mobile searches which were made on Android where, if Android didn't exist, the user wouldn't own a smart phone and the search would never have happened.
Google earns $0.9 here because they had to develop Android, but making $0.9 is better than making $0.
3) Mobile searches which weren't made on Android.
I feel like this goes in the same category as 1) because these are mobile searches that would have been made anyways, regardless of the existence of Android. The only difference is that in case 1) the search was made on Android. But for the purpose of justifying the existence of Android, they are one and the same. So Google loses 10 cents here because the would have gotten this search if they had done nothing.
Clearly Google needs category 2) to be as big as possible in order to justify the existence of Android. So the whole thing boils down to: "If Android didn't exist, the user wouldn't buy a smartphone to do mobile search".
I feel that if Android didn't exist, users would go out and buy an iPhone or something similar. I don't think the phone manufacturers would have just let Apple run away with the smartphone market so it would be in their best interest to create something competitive. But the bottom line is that Android seems like a needless expense for Google.