Surprisingly, due to architectural limitations, it isn't affected by either of the issues in spite of having some speculative execution capabilities. The G5 might be but it appears the G3 and G4 are good to go based on this detailed writeup I found.
"...the G3 and the G4, because of their limitations on indirect branching, are at least somewhat more resistant to Spectre-based attacks because it is harder to cause their speculative execution pathways to operate in an attacker-controllable fashion (particularly the G3 and the 7400, which do not have a link stack cache). So, if you're really paranoid, dust that old G3 or Sawtooth G4 off. You just might have the Yosemite that manages to survive the computing apocalypse." [1]
The way I read it, it's not immune, just harder to attack. Furthermore, Meltdown and Spectre are just two specific ways to attempt a whole class of attacks and could be improved upon especially now that the whole world's attention has been brought upon it.
So yeah probably you're not going to have issues in reality with a G3, especially given its small presence in modern computing, but I wouldn't choose it thinking it's immune either.
I wonder (my evil devil's advocate) if there are satellites or other hard-to-patch vital facilities that could be compromised with either of these vulnerabilities.
