I don't think it is too difficult to create a chrome extension that does this (disguised under something else of course).
It's an interesting thought. Certainly we know that people will download any old browser extension or mobile app without so much as a second thought, let alone actually spend time reviewing the code. We've seen people lose bitcoins due to downloading apps which give them a sparkly background or a new font on their keyboard, for crying out loud. The best defence against such a hypothetical attack is prevention; there are a grand total of less than 10 good browser add ons. Anything else is not only unnecessary but also introduces unnecessary risk.
If that's possible in a browser, I'd expect it to be exploited for banks first: there's much more money to get and they have much more users.
The vast majority of online banking payments are made through a secure payment processor, whereas the vast majority of online bitcoin payments are made through copying and pasting an address. It would be much easier to change the later than the former.