Do the VVT solenoids (Bank 1 and 2) affect engine idle in any way if they are not working properly?
I understand how a poorly functioning VVT affects acceleration, but do they cause poor idling as well?

I don't think the VVTi system is active at idle. You could quickly find out by disconnected the oil control valves.

Yes, often they can cause a rough idle/stalling when warm. The reason is that the VVT 1MZ uses valve trickery - through VVT operation - to achieve the same effect as the older, non-VVT motor did using dedicated EGR hardware.

EGR is not on during cold start or WOT; only at warm idle or part-throttle operation. So if the VVT system is not working properly, EGR isn't either and you get the same symptoms - problems at idle and WOT.

But VVT codes are pretty cut-and-dried, you'll almost always get a specific code for a solenoid or misfire codes for a whole bank.

Yes they'll cause poor idle, it happened to make my brother's GS300 idle very rough.

Once we replaced the OCV everything was smooth again.

I just checked out your youtube videos on transmission fluid changes. Very helpful. Subscribed to your channel. Thank you again.