TL DR: Should you pass? Yes. Will you pass? There's no guarantee.
For the most part, yes. It will pass that part of the inspection. There is in some states, however, a visual inspection. They will be looking to ensure the EGR, cat converter, etc, are in place while doing the inspection. They do this because the triggers within the computer which relates to these parts can be "tuned out" by an industrious person. That means, these pieces might be missing, but because the parameters of the OBDII system which notes for this are changed so that it doesn't "see" the issue. If you have everything in place as well as having the drive cycle completed, your chances of passing the emissions inspection are greatly increased.
As far as how the inspectors do their thing, yes, it is my understanding they attach a computer which reads the same parameters as what your handheld device does. As long as your vehicle has done it's self diagnostics and completed the drive cycle, you should pass. You never know what funky things your local emissions might do, though, so that's the reason I say "there's no guarantee".
One thing to note: If you "clear the codes" in your computer, whether or not ther are any codes, you have to do the drive cycle again to ensure the readiness of the system. If you do that, you will not pass emissions testing until after you've completed the drive cycle.