Should be possible but there are some caveats. If the game is huge and complex (i.e. 3D, networked, large levls, complex behaviours, etc...) then flash will probably not be able to compete with other technologies, but then if that is your target it is going to be an uphill struggle whatever you use.
Pros:
Fast to get things working,
AS3 is easy to develop in and debug (especially with the right ide - use FlashDevelop it is free pretty powerful).
Flash, despite what a lot of people think is fast, thousands of on screen sprites are no problem if you use Stage3D (GPU).
You could (depending on mechanics) easily port the game to android and IOS.
You could allow people to play a "demo" version online before they even have to download the full game.. which is neat.
The Flash IDE makes building ui and assets very easy.
Cons:
Flash is not as quick as c++ or c#... but it isn't a million miles away.
Some useful language features are missing but it is not prohibitive.
People just don't like flash.
What kind of game are you thinking of, if you were able to share with us a brief of some kind we could probably let you know if flash is up to the task.