I have used many calculators and not one was able to accurately predict infusion temps and amounts. None of them seem to take the fact that the cooler resists temp changes into account.
The calculator in BeerTools Pro specifically takes into account the thermal mass of your personal cooler, once calibrated. I've had great success with the calculation, but if it is off, you can use the error to fine tune the thermal mass and improve it's accuracy. Calculators that don't require you to calibrate your tun and then take that thermal mass into account are going to depend on luck that your tun is like the one that the guy used to develop the calculator.
The other thing to keep in mind is that you have a bit of a broader window to hit with an alpha step, than with a single infusion. You are going to accomplish the goal if you hit, at the very least, in the 158-162F range.
Will it be a different beer?
It depends on the exact question. Pulling one out of my hat, "Will a beer mashed for 60' at 148F be different than one mashed for 20' at 148F and 40' at 158F?" There's a strong probablility, and that difference is probably going to vary between systems. Or another, "Is there a single infusion temperature that will give me the same result?" Perhaps you can find the temperature that gives you the same result as the alpha rest, but I don't know what it is.