Personally I wouldn't recommend any of the cheap brand stereos. You might loose a bit of functionality, but I'd go with a Pioneer, Alpine, Sony etc etc any day. The amp will be of much higher quality than those cheap units. They suffer background hiss and things like that normally.
But yes, it's common to connect the aerial feed to the remote out/ electric antenna out feed on the stereo so it powers the aerial when the stereo is turned on.