Can I use ReactiveCocoa to write my app which includes a sub-project (existing/static library) project that doesn't follow MVVM or Reactive Cocoa in iOS?
Short: yes
Longer: There is a lot of libraries wrapping non-reactive code with reactive patterns. I advise you to look at them first : http://cocoapods.org/?q=reactive
In the opposite, using ReactiveCocoa does not impose you to code your app in a full functional-reactive way, there are a lot of bridges (RACCommand, RACSubject, ...)