[ninwa]

Perhaps we could do the reverse? Provide search suggestions if the user explicitly tells us to by beginning their input with a special character. '?' perhaps.

Alternatively, although not intuitive, if the user enters focus with the search bar through a specific key-stroke: CTRL + L for a regular URL entry, and re-route CTRL + K to our web-bar, but with suggestions.

[oconnore]

In Opera typing g + space begins a Google search. The prefix is stripped off before it's sent.

[seabee]

Your alternative method is Chrome behaviour (of course it gives suggestions even if you don't prefix with ?, but the keyboard shortcuts are there)