Yes, this will work just fine - the key works for the same version of Windows, regardless of bit-level.  You can download a Retail ISO, burn to DVD, install with it, then activate over the phone (with Microsoft NOT Dell) using the Product Key on your COA sticker. www.mydigitallife.info/download-windows-7-iso-official-32-bit-and-64-bit-direct-download-links
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.
Can I switch my 32bit Win7 Pro to 64bit using the same key from the Dell OEM 
disc?