If this were the case then pretty much all of America's political and military efforts would have been aimed at gaining control of that territory. Britain most likely would have set it up as an Indian Territory but the continuing influx of American settlers would have immediately caused tension. It is very likely that the Louisiana Purchase would still have gone through, because just as Alaska was seen as a way to surround Canada to pave the way for future annexation, control of Louisiana would have put the US in a much better position to take the NW Territory.
It is likely that when something similar to the Chesapeake Affair occurs even Jeffersonians and New Englanders will support a war against Britain to gain control of the NW. This will be a much more difficult war for Britain, because unlike taking Canada seizing the NW Territory will be extremely popular and the war is more likely to happen at the height of Napoleon's power than during his later decline.
So more than likely the US will fight a victorious War of 1807 that sees it take the NW Territory, perhaps with even better border concessions than OTL Webster-Ashburton Treaty of 1842. If the war focuses on the NW with no invasions of Canada than it may have lasting effects on Canadian nationalism as well.
In OTL the British conceded the NW rather early on for two reasons...to curry favor with the newly independent US, thus splitting it from its French and Spanish allies and because they knew holding the NW when faced with the influx of American settlers would be extremely difficult.
Benjamin