Would anyone know (or could guess) if Mate would run reasonably on a G4 PowerBook3,5 1.0 GHz with 1Gb memory?
This is guess work but it should run ok - probably be better off with older distros though and the 1Mb L3 cache should be a benefit. Try a live disk first before you install.
I don't think the issue is will it run but will you find any benefit? It's fun to try Linux on PPC but I almost guarantee you'll be reinstalling OSX not long after
I find this guide the best:
http://ppcluddite.blogspot.co.uk/2012/03/installing-debian-linux-on-ppc-part-i.html
Although the author is installing Debian on a G3 iBook, a lot of the info applies to the easy install distros.
Apart from performance, PPC Linux can take ages to set up correctly - a far cry from X86 installs which are painless.
I bought a no brand laptop for £5 at a sale last week, turned out to be a fairly well specced AMD Athlon from 2002 with a newish battery.
I popped a Crunchbang disk in it (Debian Wheezy based) and it was installed in 5 minutes - all drivers etc functional, no extra messing or hunting down issues. Of all the thousands of laptops made since 2002, Linux still just works on a machine like that - however PPC Linux, made for a small number of Apple machines with known hardware and still you might have to separately fix/enable graphics, sound, wireless, power management, trackpad, mouse buttons, hot keys, right click etc etc.