The 32-bit version of Exchange 2007 cano be used in a non-production environment only.  As such, there is no need to license the product by entering a product key.  Doing so will only result in the error "Invalid product key".

A side effect of this limitation is that you can also not enter a product key for a valid 64-bit server from a 32-bit installation such as the management tools on a 32-bit OS.  I have a PowerShell script that configures a server, depending on the roles that are installed.  However, the first thing it does for all servers is apply the product key.  This fails because I am running my configuration script from a 32-bit management installation.

I consider this a bug.  The only solution is to run the Set-ExchangeServer command with the -ProductKey parameter on a 64-bit installation of the management tools.