We can be certain that just about everything that happens at Dow Jones and The Wall Street Journal will be scrutinized, and quite publicly. It is difficult for any publication's positions and content to be completely separate from its ownership, except in those cases where the ownership really doesn't care all that much about it anyway. I am fairly certain that the next year or two will be an era of separation. However, it may be impossible to maintain that too long. News Corp. will make decisions in regard to hiring and, importantly, the purse strings that pay for everything that goes on in the newsroom.
Since Murdoch is 76 years old, there is also the distinct possibility that when he at some point (obviously no one can speculate on his lifespan) is no longer in charge, the ideology he espoused will erode into more of a corporate approach, as has happened with the empires of other media barons in the past.
It is especially difficult for a publication's editorial operation to remain independent if the owner grew up in the media and has a history of being actively involved in it. Everyone knows who owns their company and one way or another it affects ideas, decisions and trends. Even taking strong stands that run counter to ownership is likely be taken with greater tact and caution, if those involved have any designs whatsoever on long-term involvement with the company. At least that is the way this usually plays out.
Apart from the paper's internal editorial board, a five-member editorial board to assure the journalistic independence of its news coverage has been put into place. It will have limited ability to intervene but unlimited ability to voice its opinions. Its composition will change over time. Few journalists believe it could go against Murdoch and win, though it could play a role in monitoring the product.