Easily! (because someone else already did the work for us...)
After spending a lot of time trying to this with the suggested answers I came across this codeplex project Windows Input Simulator which made it simple as can be to simulate a key press:
Install the package, can be done or from the NuGet package manager or from the package manager console like:
Install-Package InputSimulator
Use this 2 lines of code:
inputSimulator = new InputSimulator()
inputSimulator.Keyboard.KeyDown(VirtualKeyCode.RETURN)
And that's it!
-------EDIT--------
The project page on codeplex is flagged for some reason, this is the link to the NuGet gallery.