I think I see now what the hangup in your thinking is Slider. In your imaginary world is the supply of money fixed or not fixed?
If the supply of money in your theoretical world is static, then, no, what you say cannot happen because like in sjfan's example for one person to be more productive it must come at the expense of another who might also have been able to use the money.
If the supply of money in your imaginary world is consistently increased then you have the same problem that is occurring now: inflation. The interest rate isn't the culprit, merely the symptom.
If the supply of money in your theoretical world is static, then, no, what you say cannot happen because like in sjfan's example for one person to be more productive it must come at the expense of another who might also have been able to use the money.
If the supply of money in your imaginary world is consistently increased then you have the same problem that is occurring now: inflation. The interest rate isn't the culprit, merely the symptom.