When I went from a 39 to a 41 on the rear of my M900 everything fit just fine, and the bike only had about 1000 miles on it. The axle was closer to the front of the adjustment range, but I still had room. You put the chain onto the sprocket before putting in the axle, so the tire can slide forward far enough to easily get the chain over the sprocket.
With the original sprocket on the bike and your chain adjusted properly, look at how far forward you can slide the axle. If you have half an inch of travel available, you have more than enough room to go up two or three teeth on the rear.