Can we build an AIR App(one code base) that can work on Android devices, iOS (iPad), run as a web application and desktop application?
The loose answer is: Possibly.
There are features exclusive to each platform that will need to be considered when designing your apps. As long as you research the features you need, check the API for those features and look for it to warn you that the feature is not available on some platform. Then you'll know if your single codebase will work.
It's not relatively feasible to expect anything short of a website to operate equally on all the mentioned platforms. Appliations tend to require branching code to handle a different platform. For instance almost all mobile devices and tablets have cameras built in but not all desktop PCs have them, etc.