OK, so now I know for a fact that once the charging circuitry in the phone detects a full charge, it immediately starts using the battery to operate and doesn't draw ANY power from the charging cable.
Last night, I charged the phone to full and I was still awake when the light turned green... I picked up the phone, played a game, went on the internet, etc. Phone held a 100% charge for a few minutes, then started dropping. After about an hour of medium/heavy usage, I was down to 94%. Which is about right for the usage I was putting in.
I plugged the phone back in and went to sleep... The dog woke me up about an hour later and I glanced at the phone... Green light. I let the phone sit as I went back to sleep for about 4.5 hours and then took the phone off the charger. It immediately dropped from 100% to 99%... then 95%, 93%, 92% and finally settled at 91%... This drop took only 2 minutes to happen and the drop from 93% to 91% took a few seconds longer than the rest as the battery sensors were "zeroing in" on the actual charge level. This 9% drop is indicative of a phone that's been sitting for 4 - 5 hours on the new battery partially idle and syncing mail, Facebook, Twitter, etc...
Now, this may be a design of the phone, but it really will not work for many people... An example is that I'm going to be driving from NY to Florida in a few months... I'm going to leave the phone plugged in when I use my GPS. Problem is, if the phone is fully charged, it's going to run off the battery and I'll have to remember to unplug and plug back in the charger to make sure I have battery left when I leave the car... Hence why a lot of people report charging the phone overnight, using it for a minute or two, and then needing to top off the battery before they leave. While they were sleeping, the phone started using the battery. This was also proven in the EVO forum thread that I linked earlier.
Could something like this be fixed via a software update? It seems it would need a firmware update to fix the charge circuitry to run off of the power source when plugged in... Either way, I seriously think this is something HTC needs to address on both the DI and the EVO...