No, don't plug the A500 into any receiver's switched or unswitched outlet. It draws too much power. If you check the back panel, or the manual, it will tell you the max power you can plug into those outlets.
The 3805 allows a total of 120w total for both plugs. So I will probably just plug the DVD and either tape deck or turntable into the 3805. Are these ok as plug ins?
Now, as the the trigger. If you want the 3805 to trigger the power center on and off, what will happen when it is powered off? How will the 3805 have 12v on it to turn it on if it too is plugged into that power bar?
The power center has switched and unswitched outlets. The receiver is an unswitched outlet - always power to it. So it will not shut down.