Unfortunately what you are forgetting about there is no XP drivers for anything. That model is too new seeing the OS options as 7 Basic or 7 HP both 64bit. Inspiron 15R Laptop Details | Dell India
There is however an option to see the XP Mode run on those editions or on older hardwares that lack support for virtualization. Besides VirtualBox the VM Lite Workstation's VMLite XP Mode
will automatically download and setup the XP Mode if not already present on the drive. The advantage over VBox however is still seeing the integrated components supported.
As far as the 64bit drivers working on the 32bit Windows? The answer on that is no! On occasion however some 32bit drivers will work out well on the 64bit however. This is due to the 32bit emulation support seen for them.
You can install and run XP on most newer boards to start with without a driver disk due to the upgrades seen a few years back allowing the XP installer to see Sata drives. But you would have to run XP without the remaining drivers for video, sound, and anything else since none were writtern as I suspected right off. That model series never saw any written to start with being too new.
The best advice is get what you are able to running on the 64bit The alternative is the 32bit 7 which surprizingly has quite more a bit backward compatibility even for many XP drivers then was seen with Vista. VBox or VM Lite would see XP running on a virtual machine(VM) there but not help you with the gaming at all.