No. The very earliest model of Power Mac G4 requires Mac OS 8.6. Some of the latest models can't even run OS 9.2.2 natively, only OS X.
Even the first generation of beige Power Mac G3 and the first Kanga "PowerBook 3500" PowerBook G3 require Mac OS 8.0 or later. (Although through some hacking, it has been claimed possible to get the Kanga PowerBook G3 to run 7.6.1. I haven't seen any writeups showing how to do it.)
To put it simply, no Apple "Gx" machine can run any version of System 7 without hacking. And even then, it's only the very first G3s. Even the first iMac G3 can't run 7.6.1.