Even if being the weakest console is a hurt to Microsoft, they could still easily come out better due to the advantage of the early launch. I just took the NPD numbers and did a few simple spreadsheet operations to make a mock "next generation". If anyone would like to try different modifications, just say so.
For Xbox 2 I take the Xbox numbers from November 2001 on and put them in November 2006... but I drop 15% of their numbers due to the disadvantages discussed. For PS3 I take the PS2 numbers from October 2000 on and put them in October 2006, adding in 10% of the 15% which Xbox 2 has lost for that month. For Revolution I take the GCN numbers from November 2001 on and put them in November 2006, adding in 5% of the 15% which Xbox 2 has lost for that month. Of course Xbox 2 shouldn't have the big loss for much of the first year, PS3 probably won't launch with such a small supply again, etc. etc. but I'm keeping things simple.
Obviously this gives Xbox 2 lower numbers than Xbox at any given age, but the early launch gives them a huge headstart as far as market share goes. Obviously through the first year they'd have 100% of the next generation market share. At the end of 2006 they have 60.3% to PS3's 19.5% and Rev's 20.2% (obviously this simulation is not reality). At the end of 2007 they have 36.4% to PS3's 42.6% and Rev's 21.0%. At the end of 2008 they have 29.6% to PS3's 49.5% and Rev's 21.2%.
Still far from first place most of the time? Sure. However, even my gloomy prediction makes them a much closer second, and keeps Revolution a more distant third.