Don't worry about imaging, then. If you do want to copy the entire drive, you will have to overwrite some critical Windows installation files when you copy back. It's no big deal if you have Windows already installed on the hard drive when you get it back, but to be safe it might be better to do the copy back when running Linux off a Live CD, because of the "overwriting Windows installation files" part.
If you copy the drive, though (and yes, it is basically open C: -> CTRL + A -> CTRL + C -> go to other drive, hope it's blank -> CTRL + V), you will copy all your installed programs along with your files. I'm not certain if it copies the registry too, but my guess is that it does. It will not copy the MBR and such, which is critical for making Windows boot and for the partitions to be defined properly. A disk image will copy the entire disk into a file, from beginning to end, including the MBR (but not necessarily your partition info). That is the main difference between a straight copy and an image. When you copy the image back on to a hard drive, it will also copy the MBR, meaning it will boot properly as well. But, like I said, if you have Windows already installed when you get the laptop back, you don't have to worry about this.
Anyway, AFAIK, removing the drive should not void the warranty. Out of all the laptops I've done that with, there is absolutely no way to tell when the drive has been removed. Just call in and ask if you can do that, because it'll save you a lot of time (usually just takes a couple of screws, piece of cake). If you can't do that, the next best thing to do is to copy only your files, because face it, it will probably take you about as long to filter out what to copy and what not to copy as it would be to just copy the entire disk, and it's a lot less risky and takes up less space in the end. Your main concern with files would be the whole Users folder in Windows 7, or the whole Documents and Settings folder in XP. If you have any other folders you commonly save stuff in, copy those too.
If you're absolutely insistent on not doing that, maybe try a backup program? I have personally never used one before though.