Nope, not when using "Rotate Around Selection." You can kind of get close with Auto Depth, but you have to watch the mouse location whenever you start to rotate the view.
I would recommend you try Auto Depth on, and Rotate Around Selection off for a bit. I personally don't like Auto Depth, but it can make it quicker to navigate when there are many objects. Just move the mouse over a object and it will rotate around that spot. Auto Depth does not have the same problem of using the object origin like Rotate Around Selection does.
With both Auto Depth and Rotate Around Selection off, the 3D view works in object mode like you desire, but you are back to manually centering the view.
There is even a warning on the linked manual page about the Rotate Around Selection setting in object mode (exactly what you are experiencing).
This may seem ideal behavior. However, it can become problematic with larger objects such as a terrain-mesh, where the center is not necessarily your point of interest.
The way I navigate in the 3D view is to go in to edit mode select a vertex, or a piece of a model; then press NumPad . to center the view around that part and head back to object mode.
You can rotate and zoom the view as much as you like and it will stay centered around the selection from edit mode.
