No. OEM copies are locked to the manufacturer's BIOS. If you try to install a Dell OEM copy on an HP or vice-versa, it will require activation, which MIcrosoft will not allow. If you want 7 on your HP, you'll need to get the upgrade from them if the system qualifies, or buy a retail upgrade - the Dell disc will not work.  
Hi, Ideally we can use license key to install window OS on to 3 systems, could any one confirm same regarding Dell Win7 upgrade OS? Regards Arun
Window 7 upgrade - How many system could be upgraded with licence key recieved 
by Dell upgrade option?