That's very likely to be used, probably in conjunction with the suction dredge already brought in. Using compressed air or water to push around the sand you want to dredge is quite common. Sometimes ships have been un-stuck from mud by injecting compressed air near the hull to break them free of suction.
As a salvage job, this isn't that bad. No waves, a good climate, easy land and water access, hull intact, on an even keel, no leaks. It's just big.
If you want to waste time on this, look up the AIS data for all the big dredges and cranes Boskalis and Smit own, and see what's moving towards the Med. Here's the Boskalis dredger fleet.[1] If those guys decide to move sand, sand will be moved.
Smit's ships include the Smit Borneo, which is a crane ship big enough to take containers off a large container ship. It's done that before.[2] If
they have to partially unload the ship in place, it can be done. Not all that fast, but it will get done.
Here's a Smit container removal job from a smaller ship, but one in much worse condition.[3]
Those guys do a lot of planning and modeling first. The idea is not to make things worse.
This is such a good idea that it actually exists and works.
Look up water injection dredging.