It shouldn't since the BBAF is driving the AF. The shutter button merely meters and takes the photo since you've disengage it from the AF process when you enabled BBAF.
Don't you have to explicitly remove focus from the shutter button?
I have not modified the actions of my shutter button so I am not a true BBAFer. I haven't tested my settings extensively but current expected results with default camera settings of one shot AF, center point only and back buttons used to modify behaviour I get
Shutter button = focus+metering+shutter
'*'= toggle drive mode; camera in one shot it shifts to AI servo and vise versa
AF-ON= AI servo, 25pt zone, case 6
As far as I've tested it looks like it is operating as expected.