No - you can keep the same washing machine as long as the adapter is sized correctly for your washing machine hose's size. The adapter pictured is a compression fitting, so it is made for "smooth" tubes like yours. No threaded tubes necessary.
As for knowing if you already have a vent, aside from busting up the concrete or wall, or going into the attic to see if there is a vent line in that wall, there is really no way to see if it is vented. You could go onto the roof to see if a vent is popping through (which I'm sure there is) but there is no way that I know of to know for sure if it is connected to the washing machine line.
The AAV approach should be fine as long as there is no code in your area against its use.