Bob Dylan .. Robert Smith .. Lou Reed .. even Jon Anderson
none of them sang with 'perfect' pitch, but they performed in such a way that if you tuned them you would most likely wreck the track.
Other (more recent) artists that have gone platinum shouldn't be heard without tuning efforts.
Let the track (and your ears) decide.
I've used a bunch of different tuning softwares. The included TCHelicon can be used for correction if done correctly (using a MIDI track for tuning) but the real question is what kind is needed and how much? The answer is in the results.