Based on the "Minimum Hardware Requirements" mentioned in the "Installation Guide" for PowerPC, the answer is YES.
Nevertheless in the real world, a one core microprocessor with less than 1GB RAM will result in a less efficient computer "feeling" slow in many aspects.
You must consider seriously what is mentioned in the given page, specially what refers to the graphic desktop environments, as follows:
The actual minimum memory requirements are a lot less then the numbers
listed in this table. Depending on the architecture, it is possible to
install Ubuntu with as little as 20MB (for s390) to 48MB (for i386 and
amd64). The same goes for the disk space requirements, especially if
you pick and choose which applications to install; see the section
called “Disk Space Needed” for additional information on disk space
It is possible to run a graphical desktop environment on older or
low-end systems, but in that case it is recommended to install a
window manager that is less resource-hungry than those of the GNOME or
KDE desktop environments; alternatives include xfce4, icewm and
wmaker, but there are others to choose from.
Anyway, there are lightweight desktop environments and several distributions based on ubuntu (lxde and lubuntu comes to my mind), which makes a difference in "speed" at the very moment that you use the computer to do something, apart from the boot itself.
You must remember that the "speed" of a computer is a sensation. Something you "feel" based on several things, not only the speed of the microprocessor and RAM.
The fast answer is YES, it will run. But you may expect a slow performance computer after all.