Bear with my train of logic for a moment, bearing in mind that I'm a big fan of several Xbox 360 exclusives.
First, the facts- The Xbox 360 routinely outsells the PlayStation 3 in North America, although in terms of worldwide sales, it now appears as if the two consoles are just about even. Call of Duty certainly sells best in the US, the one country where the 360 actually does top the PS3 on a consistent basis. And according to recent numbers, approximately 70% of CoD players use the 360 for playing any new entry. Typically, the split is 70/30 between the PS3 and 360 versions of any new CoD and sometimes it's an even bigger discrepancy.
Now, the PS3 is well known for its exclusives (no, we don't need to run down the list). The 360…well, we've got Gears , Forza , Halo , and Alan Wake , with a few other minor ones (like one of my favorites, Lost Odyssey ) adding to the console's appeal. But Gears and Forza combined could never hope to reach Call of Duty sales numbers, and the Halo fans have to face up to facts…this is a CoD world these days, although Halo 4 is slated for the fall. The bottom line is that the 360 exclusives, regardless of what anyone says, don't have anywhere near the appeal Call of Duty has on a country-wide basis. I mean, it's not really even close.
Then you start counting up the sales of the 360 versions of the last four CoD entries…the numbers are astronomical. Of course, the PS3 benefits to some extent as well, but it's hardly the same thing. Furthermore, as CoD is basically a community event (multiplayer is the major draw), newcomers are probably enticed to purchase a 360 because the majority of their friends likely play CoD on Microsoft's system. So it's very likely that a great many people out there did in fact purchase a 360 only for CoD in the past few years, and given the sheer size of the numbers associated with that franchise, and Microsoft's general success in this country…
Now, if you just took away CoD and didn't factor in the profound impact that franchise has had, would it really significantly affect 360 console sales? I honestly think it would.