Is it possible to create a Windows 7 installation disk that can install either the 32-bit or the 64-bit version from the same disk? I would like to be able to install any version and any architecture of Windows 7 without needing to have separate installation disks or flash drives.
Yes, this is possible. You will need source disks or ISOs for both the 64-bit and 32-bit Windows 7 installers. Any edition (Pro/Home/Ultimate) will work, as there's a way to configure the installation disk to let you choose any edition. If you don't have disks, you can find links to official ISOs here.
The easiest way to integrate the installer disks is to use WinAIO Maker Professional, which is free (as in beer) software which will automatically take your two ISOs and integrate them for you.
Just click on the "AutoAIO" button near the bottom right, select your x64 and x86 ISOs, and it will create an ISO with both versions integrated. If you prefer to install from a flash drive, you can copy the installer to a flash drive just as you normally would.