TWA will work in a signal chain with other pedals like the AD-10! You can certainly run the output of TWA to the input of your Boss unit.
If you do install a mic pickup, make sure that's running to something other than TWA, as TWA and a mic pickup system will create a feedback loop!
However, when running a cable out of TWA, you can set TWA to TWA or DI, where the driver on the guitar's body is muted, but the a blendable signal continues to run through the output.
You can also run pedals before or after TWA, just a heads up!
Yes, you're understanding the input signal path correctly! Guitar>TWA>AD-10.
And yes, pickup systems that run on a condenser mic internally will result in uncontrollable feedback.
Soundhole pickups are okay, just not mic only system. Mic blend systems will work as well.