maybe.
being a big OEM they will have code int he bios to link the disc to them.
They have to implement this for OEM activation (slp, system-locked-preinstallation)
They may choose to use this as part of the cd boot sequence.
in short, if the cd boots your pc, then it will install windows on it. it will probably automatically partition your hard drive too. and format it etc, allwithout prompting, be prepared for this. pop the cd into your laptop and go browse the disc contents...look int he i386 folder for a file called winnt.sif. open it up in notepad. if it has lines like oempreinstall=yes then they have customised the cd and your chances are very low.
once installed though, it will try to automatically activate using oembios files in the windows directory, querying the bios for a specific string. if this string is not found, then it wont be automatically activated.
you will have to phone ms and explain yourself.
if you have a windows xp key code, and it is off a sticker on the machine, then you should quote this key code to microsoft.
if your windows xp you bought was full retail version, then that key code cannot be used to activate the oem copy of windows xp as supplied by dell.
p.s. if you run the windows on your laptop and on your desktop, and dont clean it off one of them then you are breaking the terms and conditions of the cd.