This concept is already in work by BP.
BP has tried two variations of this methods so far. The first was a larger 400 ton, 4 story containment box. The second was a 5ft tall 4ft in diameter box that weighs less than 2 tons. BP has reported that the use of the larger containment box was abandoned because of Ice crystals of frozen hydrates accumulated at the top of the device which prevented oil from being pumped from the box. BP also reported that the dome became buoyant and began to float.
BP's reported reasons for the failure are questioned however. It has been suggested the that pressure from the oil and methane leaking from the well was so strong that it made the containment box float.
Being that this was not a closed system, this technique required a strong pump to suck in a combination of seawater, gas and oil with enough pressure to create a vacuum.
It has been suggested that, even given what now is a being grossly underestimated rate of flow of 5,000 barrels per day, that there is not a pump on earth capable of pumping enough oil to create a vacuum capable of sucking oil shooting out of the well. It should be stressed that the calculations given for those estimation used only hypothetical velocities and pressures.
A smaller containment dome, called a 'Top Hat' has also been lowered to the ocean floor. BP reported that the smaller device would be much easier to heat and prevent the formation of methane Ice Crystals. However, once that 'Top Hat' was lowered to the floor it's use was not attempted. There have been no media reports of why the smaller 'Top Hat' was abandoned, only that BP began working on a tube that would siphon oil from the leak.
There have been reports that the smaller 'Top Hat' failed but main stream media now reports that the device is in place and is ready to be tried at a future time.
The feasibility of smaller device working is question, with the same uncertainty of the existence of pump that create a vacuum strong enough to suck the oil after it leaves the leaking pipe begin raised.