The wording on the "free" Win 10 upgrade is literally that. An upgrade from an existing Windows 7 or 8/8.1 installation on your computer. If your computer is a 32 bit copy of Windows 7 Home Premium, for example, the upgrade to Windows 10 will be a 32 bit version similar in features to your copy of Home Premium. Same for Pro, Basic, Business, Ultimate, or Enterprise editions. Assuming Microsoft releases that many editions for Windows 10. You'll likely end up getting a version closest in features to whatever you have installed already.
In short the upgrade path will be 32 bit to 32 bit, 64 bit to 64 bit, version to version. The only exception to this would be if you bought a specific version of Windows to upgrade to, and no, to answer a quick question, you cannot install a 64 bit OS on a 32 bit chipset, but you CAN install a 32 bit OS on a 64 bit chipset. The catch for that being you'll limit your computer to 4GB of usable RAM because that's the RAM limit for 32 bit computers. Hope this helps!