Interesting... It looks possible under ideal conditions in a modern aircraft. (I attempted a basic simulated flight in google-earth flight simulator-vid below)
Edit: The service cables mentioned in the other answer would also represent a substantial problem, but they were missing from the model.
Assuming you can get through the gap, the main issue for the maneuver seems to be the ridge immediately behind the bridge in the valley, which is marked in red in this shot, (and then you've got a second ridge behind if you continue a straight climb out)
Obviously it puts a constraint on the climb out path if you approached from the sea, or the path of the descent if you started in-land.
It looks like you would have to follow a fairly specific path to avoid the ridge, though if you knew the terrain and the aircraft well, it would make it a lot easier.
If you started inland, a direct approach would include avoiding these ridges on the way down, and a fairly hairy check of the descent as you cross under the bridge... There would presumably be some ground effect benefit when attempting to obtain positive rate of climb over the beach/ocean.
Edit: adding the utility cables makes it look like a very small gap indeed!
I noticed that Google Earth has a flight simulator, so after a couple of crashes into mountains, I fumbled a path... (I hadn't worked out the flaps, or power keys at that point, so its totally with defaults as set when selecting flight sim mode)
Edit: following @Cpt Reynolds suggestion in his answer above, this is one route through;
Or alternatively, come in with as much speed as you can stomach, and just ride over the ridges;
It was done using the SR22 model (310 horses, cruise 185kts);
If you want to have a bit of fun trying the various approaches... I used this model of the bridge from sketchup, and imported into the google earth desktop app.