Well, that all depends on what you mean by "recovery disk" and by "back-up of my computer".
If you're talking about the recovery disc that came w/ the computer, probably not. Those usually have all the software, etc, saved on another partition of the drive.
So - what's your setup - is this disk w/ three partitions you're talking about an extra HD in the computer? What do you mean by "back-up"?
If you used cloning software like
Clonezilla to create an image of your HD and stored the image on an extra/external HD, then you should be able to use the same software to restore the image to whatever partition of the disk you like, so long as it is equal size to or larger than the original.
Does that help out at all?