kea, welcome to the forum! We need a little more specifics to properly answer your question. If it's your backup program's boot disc, and you're using the same backup program & version, then yes you can.
If you have say, Windows 7 64 bit on both computers, and created a boot/repair disc on one, yes it probably will.
But if you've created a set of recovery discs for your desktop (usually between three or four DVD's) to reinstall your system, no, you cannot do this. That install is only for the computer that it came with. Usually, only OEM's (Dell,HP,etc) offers you the option to make these discs ASAP after you purchase the computer, so that you can do a "fresh install" at any time you wish. Also, these computers usually ships with a recovery partition, which you can boot into, and accomplish the same thing, only a little faster.
The discs are best used when installing a new hard drive, or if the recovery partition has been deleted or damaged.
Depending upon the make/model/year of your notebook computer, you may already have this partition installed. Consult your manual/OEM site for details.
Let us know how things are going, and always feel free to add additional info to help resolve your issue.
Best of Luck,
Cat