I'm curious if I need to turn this shaft down any or if I should be fine. Tapping it to a 5/16-18 thread which measures .3140 and the rod measures .3400. It'll be a pain in the *** if it needs to be turned down, and that's why I ask. Your thoughts?
Your post doesn't make sense. You are cutting threads on the outside or tapping a hole for threads? I'm assuming you are talking about the diameter being reduced to cut threads with a die.
5/16 is 0.3125, so not sure where you got either of those numbers from. You are only about 0.030 big. Not ideal, but a thread die would probably work fine. Go for it if you don't have any options.
So you're either asking a die to form the major diameter of the thread, which it isn't designed to do, or more likely you'll end up with a thread with the correct pitch but an oversize major dia, which won't thread into a standard female hole.
Do it right and either buy the right size rod to start with or turn it down.
FYI a loose clearance hole for a 5/16-18 bolt is only .332 dia, still smaller than your stock.