The simple answer to this is no, you cannot upgrade a 32-bit computer to 64-bit.
If you are running a 32-bit computer, you can only use the options to upgrade to another 32-bit version of Windows 7 (like say from Home to Ultimate).
A more expanded answer is you can perform a Windows 7 32-bit to 64-bit upgrade if you upgrade the other components of your computer, like your processor and motherboard. That's the key here. A 32-bit processor won't be able to run 64-bit programs, so trying to do so will more than likely cause the program to not run at all. In terms of trying to format a 32-bit computer with a 64-bit operating system, it is likely that the program will notify the user that the OS will not be able to run on the system or that there will be significant amounts of problems if the procedure is continued.
The correct course, if you want to upgrade, is to upgrade your computer components. You will need to do the research on checking what type of motherboard you have, as well as looking into motherboards and processors that run on 64-bit technology. Then you will need to make sure that current components will be able to run on said new motherboard.
You will also need to backup any existing files, programs, and documents, making sure to note which have possible 64-bit versions.
If you would like to upgrade from your Windows 7 32-bit system to that of a 64-bit, just make sure you've prepared to take all the necessary steps to do so. Doing an upgrade will mean you will need to reformat your computer. Always make sure you have a current backup of your system and always make sure you have the products keys or any type of access codes handy so you don't have to look around for them.