Here are the hardware numbers your looking for during that time period. These are all American.
Week before Halo 2 (No games of note)
XB - 118,000
PS2 - 122,000
GC - 56,000
Week of Launch
XB - 190,000 +61% (Halo 2 sells 2.5 Mill)
PS2 - 185,000 +51% (No Games of note)
GC - 77,000 +37% (No Games of note)
Week after Launch
XB - 256,000 +35% (Halo 2 sells 732,000)
PS2 - 245,000 +32% (MGS 3 sells 221,000)
GC - 110,000 +42% (MP2 sells 139,000)
2 Weeks after Launch
XB - 263,000 +2% (Halo 2 sells 377,000)
PS2 - 262,000 +7% (MGS 3 sells 119,000)
GC - 147,000 +33% (MP2 sells 66,000)
As you can see here, Xbox got a good jump of 61% with Halo 2 but PS2 was able to get a good jump of 51% and the GameCube also had a good jump of 37% and these were without any games. It can be assumed that the Holiday season must be selling these systems more than the recent games. The following weeks see relatively large releases for both competing systems but Xbox continues to outsell them. I think that Halo 2 really helped Xbox with selling but not on a huge scale. My assumption would be that the increase in sales would be similar to GameCubes were it not for Halo 2. So an increase of 40% the first week, then more along the lines of PS2 or less for the following weeks so maybe 30% then possibly a decrease the next week.
Because of the state of the info we're dealing with, being several years old and highly incomplete (games missing) it's difficult to tell. It's also hard to distiguish due to the holiday bump all systems receive.
On a side note I find Halo 2's legs to be incredible. The game just kept selling.