Timecode video and audio is a whole other thing costwise.
I'm not trying to dissuade you from using an external device - I've done it myself for a 20 minutes or more continuous shot - what I'm trying to emphasise is that if audio and video from non-timecode devices does not sync, it doesn't mean that there's something wrong with one or the other. To get it to sync you have to go to a bit of time and trouble - and depending on the devices it might even be hardly any - but it shouldn't be a huge amount (IMHO). If people have got good results with the H4N then that's encouraging. But because of possible variations in clocks between devices, you can't necessarily expect an identical result.
I'm not trying to dissuade you from using an external device - I've done it myself for a 20 minutes or more continuous shot - what I'm trying to emphasise is that if audio and video from non-timecode devices does not sync, it doesn't mean that there's something wrong with one or the other. To get it to sync you have to go to a bit of time and trouble - and depending on the devices it might even be hardly any - but it shouldn't be a huge amount (IMHO). If people have got good results with the H4N then that's encouraging. But because of possible variations in clocks between devices, you can't necessarily expect an identical result.