According to PWInsider.com, WWE did give Daniel Bryan the option of going home on Monday night when he learned his father had passed away, but Bryan insisted on staying and performing on Raw.
The angle done with Kane was to get Bryan off TV early into the show, so that he could be with his family. The angle was not done to write Bryan off TV for any specific amount of time, and the impression given is that Bryan will be back on Raw next week, but the angle was done to give Bryan the option of taking however much time he might need to deal with his father's passing. WWE officials are reportedly perfectly fine with Bryan taking off until Extreme Rules if he wants to.
With regards to Extreme Rules, the feeling in WWE is that the Kane angle on Raw went over so well that it might be better from a story line point of view to keep Bryan off TV until Extreme Rules to give their bout a more underdog vs monster feel to it.
For what it's worth, WWE.com did note in its last story line update on Daniel Bryan that he is "insisting" on being at Raw next week despite his "injury."