Like Clarice, I can hear someone whisper on my deaf side.  And, as she mentioned, it's really just an "illusion"; I'm not really hearing through my deaf ear - just feeling like I am.  
BAHAs, like most hearing devices, aren't perfect.  They tend to pick up all sounds; not just give you the ones you want to hear.  Filtering out unwanted noise/sound is difficult for them.  So there are limitations in noisy and/or crowded environments.  But improvements are being made all the time.  When I got my first BAHA device (a Cochlear Divino) in 2008 it had what is referred to as two "channels".  A few years later when I upgraded to the Cochlear BP100 it had 12 channels (the Oticon Ponto Pro had 10).   The more channels a BAHA device has, the better is it at filtering out unwanted sound because there are more "places" for it to "go".  There is a huge difference between my one channel and my twelve channels.  My Divino also only had 1 setting; my BP100 has 3 settings.  That helps too.
And new devices - by both Cochlear and Oticon - are being introduced all the time.  The technology just keeps getting better and better.
Jan