I have Swype on all my devices, and --
-- yes, I was able to see it.
And it works exactly the same way in Gmail, when writing a message.
And it works exactly the same way in Google Chrome, in the search bar.
And it works exactly the same way in SMS app, when entering message text.
And it works exactly the same way in Contacts app, in the search box.
This is on a Galaxy Note 2 with 4.1.2 (just what was closest).
As I already wrote, Android apps don't really interact with input methods (soft keyboard), so this behavior is something Swype does on its own. I never noticed before, btw