Most likely the opposite would happen. With Android divested from Google, it would lose access to huge amounts of its R&D options. This means it’ll need to generate more money to be able to sustain itself and future growth. Companies aren’t going to want to pay more for Android and will start to spin off Android into their own custom versions that will more likely be more locked down, not less (for their profit maximization).
In the end, it would hurt Android and the smartphone market as a whole because this could cause Android to collapse, leaving iPhone the only option. No one could be able to compete because no one would buy a different smartphone. Smartphones are bought because of the apps they have (think of how many functions you use that need an app and can’t be done on a web page. Banking, delivery apps, taxi apps, discount programs, government, etc…). Now, try telling people they could buy a different smartphone but won’t be able to use any of those functions. No sale, one of the biggest issues to happen with the Windows Phone, the Sail OS phone, Firefox OS and why they fail. And companies won’t make apps for those phones as there aren’t enough users to justify the cost of making (chicken and egg problem).
A break up wouldn’t help the market, and would really be handing Apple a monopoly for smartphones on a silver platter.