Exchange 2007 is 64-bit. So, if the hardware is already 64-bit, then the equipment will likely support it. Other variables include disk space and memory requirements.
“Upgrade”? no. You cannot “upgrade” exchange 2003 to exchange 2007. If the hardware requirements are met for exchange 2007 as Labnuke suggested, you CAN format the drive and install exchange 2007 from scratch, but no, you cannot do an “upgrade” installation. Period. Of course if you have existing mailboxes (which I suspect you do) you will want to do a migration instead. Install Exchange 2007 on another server and move the mailboxes over to the new server.
Recommended to build a new Exchange 2007 on Windows 2008 and then perform migration. Upgrade is not an option.
Nope you cannot do an in-place upgrade from Exchange 2003 to Exchange 2007. If you have hardware constraints then you can backup the mailboxes to a PST, remove Exchange 2003 and then install Exchange 2007. Use the new Powershell in Exchange 2007 to restore the mailboxes from PST back to the new mailboxes in Exchange 2007.