No. An Upgrade licence requires a valid licence of a previous Windows version. If your new computer doesn't come with one (and I'm not aware of any new computers that come with XP or Vista), then you cannot use the Windows 7 Upgrade licence and will instead have to buy a retail licence. You also cannot use your current XP licence since it's an OEM licence and thus permanently tied to your current computer.
You might be able to get a second-hand XP or Vista retail licence from someone for your new computer, but the cost of that plus the cost of a Windows 7 Upgrade licence might well end up being higher than if you just bought a full Windows 7 retail licence in the first place.