New 347 drive without tune?

there are a lot of unknowns with your tune right now. Dyno time with a tuner is great insurance and peace of mind. Plus you more than likely will extract more performance from the motor after it's been tuned. You didn't mention any details about your fuel system which is very important, plus ignition and timing. A tuner can tell you if you have enough fuel throughout the power band, you could lean out the first time you past lets say 4500 rpm and then you could hurt the motor. Like i said...lots od unknowns. I would save $ quickly for a tune. Regarding the tb, I never fix anything that isn't broken! That's me though

run base timing at 12 degrees , fuel pressure at 39 to 41 with vacuum off and plugged and it should be fine to drive , but I wouldnt beat on it till you get the air/fuel checked with a wideband

You should be fine, people been running 5.0's worked for years before dyno's or wide bands even existed.
2002's advice above is pretty good. Make sure to run 92 or better gas. You can experiment with a little more timing, if it pings back it down again.