I certainly hope it would help, though I'm not confident it will fill the gap. Thing is, if words and rational explanations would satisfy the other person, tone of voice wouldn't matter in the first place.
Geniferous is absolutely right: One thing I've learned the hard way is that people - especially (but not only) NTs - are built to respond automatically to certain cues like tones of voices, facial expressions, gestures, etc. Therefore, the absence of those cues must have some effect beyond what words can compensate for.
More broadly, tone of voice can be the exception that proves the rule. With some NTs, you have to use so much sugar coating and soft soap that the bad news is twisted beyond recognition...perhaps even by the recipient. People may miss important information because it's so obscured.
Especially if they're not the most sensitive people in the world but people talk to them as though they were, because those people are afraid of underestimating how sensitive they are and getting ignored, screamed at or worse. Not to mention that all that sugar and soft soap doesn't come free - people have limited amounts of emotional and mental energy, after all.
So, gentle tones of voice and even other things like subtle phrasing, understatements and the like aren't even close to perfect fixes. They carry costs and problems of their own.
The more NTs (and even Aspies) who take bad news personally, the more informational and emotional issues we're going to have, one way or another.
What do you think?