Yes it's possible to use adjustable shocks with those springs. Just about every shock out there will not change your ride height.
If you really want to be picky and technical, you already have coilovers since the springs are wrapped around the shocks. But in the way most people use the term, no, you still won't have coilovers. Adjustable shocks simply means you can adjust the rebound. There is no height adjustment. Coilovers are height adjustable. Some are only height adjustable, some are both height and rebound adjustable.
If you just want new shocks, you need something that can work well with those springs. I'd recommends the Koni Yellow Sports. ClubCivic is selling them for $350 shipped right now and that's one hell of a deal on one hell of a shocks.
If you want to be able to adjust your ride height, you'll need both new shocks and a coilover sleeve kit like Ground-Control. Or you could buy a full bodied coilover kit that comes complete with threaded shocks and springs.
