Thanks to an ex-Tek field engineer, I managed to get a copy of the software.
When you get down to it, you can use an GPIB card in a modern system and use it to scarf the data down for analysis. However, this is a nice self-contained system that uses the scope screen for the display and doesn't need a keyboard to boot.
The software does indeed add FFT to the scope, along with waveform math and and trigger capability that lets you create a waveform template and log any events that fall outside of it. It doesn't mesh seamlessly with the scope UI, but it's not too bad.
I've added a SCSI disk to the Tekmate since it's BIOS supports it, once an Adaptec controller chip is plugged in. Freedos doesn't have the partition limitation that the old DOS versions did.
Haven't had any success getting it on a network yet. I have a version of XFS which is an NFS client that allows DOS to mount an exported directory as a drive, but it's not working yet. It appears to mount the NFS export, but Freedos doesn't see it.
If you have the right GPIB card and an old ISA motherboard, you could use this software with any of the Tek 24XX DSO scopes.