That would be considered a "deep" hole: depth to diameter greater than ~10. Yours is 32. How much do you care about size, roundness, surface finish, straightness, location - generally considered as the "tolerances".
Why don't you just try it and see what happens? I'm sure you have a preferred lubricant - or ask here what folks like to use (I use RapidTap for about everything).
If you want it to be pretty good, start with a center drill, followed up with 19/64 drill bit about 3" deep. Then bore it to .314". Then drill with a regular length 5/16 drill bit - clear the chips really often, and plenty of lube down the hole. If the work starts to heat up, stop and let it cool. Then change to the long drill bit and clear chips really, really often (say every 0.05" you'll get the hang of it - just don't let the chips pack in the flutes), plenty of lube and let it cool if it starts to heat up. Cranking the tailstock wheel will get old in a hurry. You can slide the tail stock - set up a rhythm(slide, lock, 1/2 turn, unlock, slide, lube, slide lock, 1/2 turn, . . . ). Of course a tool post mounted drill chuck is nice (still a lot of cranking).
Drilling half way from each side is good (and will be much faster), if you can tolerate the discontinuity in the mid-point (back to what your tolerance is).
Let us know how you make out. David
