Does the value of $g$ change inside a dense fluid? How would the time period of simple pendulum change when immersed in water?
The value of $g$ wouldn't change (assuming you are doing this experiment at approximately the same height above sea level as you would test an unsubmerged pendulum).
That said, the results of the experiment, and the period absolutely would change. The pendulum would have a buoyant force acting on it to slow down the movement. The density would also increase the effects of drag, so you would slow down quite a bit due to that as well.