Admittedly:
1. Wikipedia has more "users" than Firefox.
2. Despite this, the donations Wikimedia receives are only about a fifth of Mozilla's budget.
However, people use their browser far more than they use any single website and hence might be more willing to donate more to Mozilla. (For example, I love Wikipedia, but I've gotten even more value from Firefox.)
Overall, this would be unlikely to cover all of Mozilla's expenses, but I'd also be surprised if donations (after such a campaign) would be less than 10% of current revenue; in any case it'd be a valuable source of diversification.
It's possible that the legal relation between the Foundation and the Corporation doesn't make this possible.