I don't see why, especially if the peer to peer software is a service or
something that doesn't use the interface, Kubuntu is simply Ubuntu with
KDE default and KDE apps. Like Xubuntu uses Xfce for slower computers.

Exactly what kind of peer to peer network are you going to be doing?

One machine will be responsible for handling intewrnet traffic,one machine will
be a library and the third will be a graphics workstation.All machines will be
linux;the library and worksatation will be ubuntu 6.06 and the internet machine
will be a kde unit, All are older machines and two are thunderbirds and the
internet machine an IBM pent 111.

The machine just need to have enough resourses. that is processor speed
and ram to run what you put on them.
Thay will all communicate when set up if Linux without to much problem