I don't think Blackberry can do this on its own. Microsoft will need to help them to do that and with the speed at which Microsoft is bringing basics like cut/paste, multitasking and notification to its user base, a splashy, well placed ad will grab a lot of fence sitters, especially those on Sprint.
Blackberry would have to bring Notification, Instagram, Facebook/twitter integration and LTE. It'll be half way there and its quite possible Microsoft would feel BB breathing down its neck. If this new Blackberry is easily integrated on corporate BES servers, then oh yeah, the battle is on. Windows Phone 7, 7.5 or Windows Phone 8 cannot cannot be used with Mobile Iron. No api's for it. But Blackberry, IOS and Android can. How can they be so flatfooted on this?
One other thing, all those developers that MS courted all be heading back to what they know. Microsoft needs to quit treating this phone like they do their browser. Take some risks.
Moreover, if, I mean WHEN the Verge, Engadget, TechCrunch, ZDNet, Paul Thurrott and the usual haters of all things Windows Phone get about comparing the two platforms, singing BB praise as I know they will, WP might find itself in 4th place for a little while, again. Not like that all by itself will affect US but again, fence sitters and those without brand loyalty will be lost. More than anything WP needs NOTIFICATION center. A really good one. It also needs a better backup system. What we have now seems ill conceived. So in short, it could happen.