I think it would. I'm not very used to "so", but seems to me that it's like this:
In affirmative sentences:
- He runs so fast = Ele corre tão rápido (admired with his speed)
- He runs that fast = Ele corre rápido assim (comparing speeds)
- He runs too fast = Ele corre muito rápido / rápido demais (too much speed)
Now in negatives, it seems a little different:
- He doesn't run so fast = Ele não corre muito rápido / tão rápido (his speed is not very good)
- He doesn't run that fast = Ele não corre tão rápido / rápido assim / tão rápido assim (comparing speeds)
- He doesn't run too fast = Ele não corre muito rápido (his speed is not very good).
Just to add, you're overall right but for negatives "that fast" isn't necessarily comparing speeds unless there's a specific context where there's another speed for comparison. We'll often say "he's not that fast" even without a concrete speed to compare to, as another of saying he's just not very fast at all. It functions very similarly to "so fast" and "too fast" in the negatives.