More than possible, it can be fun
But it does require a little more patient experimentation. Try taking photos of the same scene with the strobes turned off, then with them on low power in different positions, then with high power in different positions. Look at the results on the computer to get a better idea of where the backscatter is coming from. Look up "close focus wide angle" techniques and think about framing that minimises the amount of water in your background. Or, move your strobes so the light only falls on things close to the camera. I often shoot with the lens pointing up and the strobes pointing down at the reef. There's no point lighting the water when there's all that dirt floating around.
If you live locally and get to know the conditions, you will get photos on good days that noone else gets. People don't travel to cold water locations with variable conditions because the chance of getting a "good" day is too low and even then the vis isn't crystal clear. Equally don't be too disheartened by the fact that none of your photos have red fan corals on pure blue backgrounds.