Sorry to say, yes it will.
I'm pretty sure you've noticed already that you have to lift your car fairly high to get the jack stand to even go under the car, right?
If you stand back and look at the car while it's sitting on the jack you'll see it's sitting at a pretty steep angle. That's all well and good while it's on the jack because it's designed with some flexibility into it. The jack stands are not. They are VERY rigid and don't take too kindly to any sideways forces on them.
I guess if you're only doing one side at a time, you could use just one stand at a time, but it's putting an enormous amount of strain on your unibody leaving the car like that for any extended period of time. Want to see what I mean? Open one of the doors while it's up on the jack and then try and close it. Notice it sounded different? That's because the whole car has twisted slightly and the door doesn't quite line up properly.
Leaving the car in that twisted configuration for too long could cause permenant damage that I wouldn't want to be the one to pay for sorting out....
Personally, if it's only cosmetic stuff you're doing, I'd wait until you had two jacks to do the job with so as to create even stress loading on the car.
