Yep. The stock radio had a timer circuit that would allow it to power up when the button was pressed even with no ignition switch signal. Pretty much no aftermarket head unit will have this feature.
I just recently installed an Excelon unit that is a couple 'steps' below this unit. Great unit. I went down the tier a little bit because I wanted the dedicated preset buttons for radio stations. The only real difference between mine and yours is the faceplate, and that mine is from a higher line being an Excelon.