Does the order of playing the single player or co-op campaigns matter

GlaDOS seems more interested in dividing Blue and Orange than picking favorites, and will show favor to either Blue or Orange. In the Yogscast, GlaDOS awards Orange "five science collaboration points" in one level (10:27 in), then awards the same to Blue in a later level (11:45 in):

In a later episode, GLaDOS states that:

• the challenge would present a challenge for one of the two given one's performance so far, but doesn't say who (0:00)
• the two form an excellent partnership with one handling the cerebral challenges and the other "ready to ponderously wander into action should the test suddenly become an eating contest", again doesn't say who is better (5:28)

But the smoking gun, as it were, that she doesn't necessarily favor Orange comes at 9:00 when she states:

To reiterate, this is not a competition. Still, if it were, Blue would be winning. [inaudible] Blue receives five science collaboration points.

So whether it's dependent on performance is possible (although unlikely if you watch these videos), but she doesn't seem to have a complete disdain for Blue.

Explanation

In the entity list, there is a linked_portal_door for this purpose; it is used in the Death Trap (in map sp_a4_finale2.bsp):

This entity is designed to link two separate, distant areas together without any clear transition between the two. This entity is exclusive to Portal 2.

It is used in Chapter 9, in the Chamber 75 Death Trap with all the crap turrets. The room is actually completely separate from its supposed surroundings. It is the only use of this entity in the final version of the game, though commentary states that it was used a lot during the development of the title to link chambers together.

I guess that the development team first made the rooms separate so that they could wipe a bad room, then connect them later when the levels were more perfect, and I suppose that this room didn't fit.

Pictures

Here is a picture of the Death Trap that isn't connected to the other rooms:

Near the threshold and a tiny step (noclip fly) to either side:

Video

You might want to skip the commentary and long walk and go to 04:30. From here on he shows the box from outside at the three locations (before box, in box, after box); he first does this slowly, then at a later point he goes between all of them in quicker succession. This might show the trick better than above pictures.

Thanks to Jon Ericson in the comments for finding this video.