It might be possible, in a particular context. I have the impression that many users of Web VPython are not aware of the following (from the first page of the Help):
While editing, press Ctrl-1 (Cmd-1 on Mac) to run your program in the same window. Press Ctrl-2 (Cmd-2 on Mac) to run your program in a separate window, which lets you view your program and its execution side by side. If you change your program, press Ctrl-2 again in the editor display to re-run the program with the new changes.
It should be possible to eliminate the blue bar in the header, but only if you start the program with Ctrl-2. I'll look into this.
I'll comment that I find it very useful to use the Ctrl-2 option, for two reasons: 1) Seeing the program run while viewing the code can guide needed changes to the program. 2) Ctrl-Z to undo code continues to work during multiple uses of Ctrl-2, whereas if you leave the edit screen to run the program, when you return to the edit window Ctrl-Z won't restore earlier code.
Bruce