Couldn't you have a toolbar or similar on top instead (or in addition to the back button thing, thus getting rid of the even more annoying popup)?
The idea is interesting, nevertheless, but the user experience could use some love.
(And no, I'm not going to use it. DDG is my default search engine, and the !bang searches there cover all my needs)
For me, it is easier to prefix my search string with !g than to hit the back button. Especially if I already navigated a few pages through DDG results.
The back button is also an annoyance when, for example, I had an open tab, wrote a search string into the address bar and hit enter by mistake: I'd want to get back to the page I originally was at, so I hit back, and I get your search engine selection screen.
Isn't that intuitive in that case, I'm afraid.
The idea is good, but... I don't think it'd work well for this kind of thing.