Can I switch my 32bit Win7 Pro to 64bit using the same key from the Dell OEM disc?

I have a new laptop with Win7 32 on it but I really wanted 64 bit - I missed that detail. I've read elsewhere that the key for 32bit is the same for 64.

So, can I download Win7 64 Pro (same version, just 64bit) and install it on the laptop using the Win7 32bit key on the OEM disc?

Thanks.