If you remove the EGR actuator at the end of the system, then all the rest of the stuff in between becomes teats on a boar.
The ONLY thing the TVV and BPT does is modulate the vacuum to the EGR actuator. So if there isn't any EGR actuator, then there's no need to modulate the vacuum to it and both the TVV and BPT devices become useless. You don't have to remove them, but there's no reason not to. Just plug the vacuum source on the throttle body, and if you remove the TVV, you'll have to plug the coolant hole where it used to be. Or you could leave the TVV in place just to keep the coolant from running out, but don't connect any vacuum lines to it.
Now, about the heating plate under the AAR... It also serves to heat the AAR itself, so it does serve a second function other than the EGR. But my PO had removed my heating plate, and I never really noticed any problems. Being in a cooler climate, you might find that your AAR will open up some and raise your idle even when you don't want it to do so, but where I am I did not have that problem.