Tiger Woods will do just fine if he stays out of his own head. With the scandals that followed him around for so long this man has had to knock himself down and then build himself back up. He will compete at a high level to prove that he is back and someone not to mess with on the gold course.
There are these ridiculous expectations of Tiger Woods, for many reasons. Tiger used to be a phenomenal golfer. The reason is no longer great is his own fault. He is the only reason for his demise. He let his personal drama (that he created) interfere with his work. He will never achieve elite golfer status again. There is far too much pressure on him to do so. He can no longer handle it and is no longer driven to do so. He does not care to win. Until he truly wants to be an elite golfer, he will just swim amongst the mundane.
Tiger Woods just had back surgery 4 months ago and will not be 100% for the British Open in my opinion. He also might be quite rusty so it will be a tall order for him to do well in the British Open. I would not expect him to return to form until at least 6 months after the back surgery.
The British Open has been his weakest major tournament even when he was playing at his best. The courses, for the most part, aren't set up for his hard hitting, long driving game. Combine that with his back injury and his poor showing at the last few tournaments, and I predict he won't make the cut.