As well as the gasp reflex, there can be massive vasoconstriction, and sudden cardiac arrest. In any case, CPR must be started ASAP, since some victims may appear to be dead, yet may have severe bradycardia and peripheral vascular constriction, and are likely to respond to prompt CPR.
In Florida, (as in many coastal areas) one of the most common causes of drowning is rip currents. A member of THT and his wife were caught in a rip current off the coast of the Carolinas a few weeks ago--He survived, she did not.
There is also the issue, that unless you are a trained water life saver, you may be putting yourself at great risk by going into the water. If possible save the person from a boat, and take care not to make the situation worse.