Hi SeeSaw,

The effect on the ocean depends upon the oceanic temperature profile with depth as well as the strength of each storm. A hurricane can churn up the waters sufficiently to have a 8-10 day recovery period. Tropical storms and depressions have a weaker impact, largely due to the weaker winds (it is the winds of a storm that draw the energy and moisture from the sea surface & underlying waters) and weaker transport mechanisms for the energy found within these storms. Major hurricanes likely have a larger impact, with category 4 torms having been shown to churn up the waters all the way down to 200ft. Usually, the cooler waters below the surface get warmed up, while the near-surface waters cool down -- this suggests mixing going on within the ocean.

If a series of storms were to pass by in close succession, the waters could be affected enough to temporarily keep other storms in check, but the recovery period and fact that storms usually don't occur in rapid succession suggest that any such impact will be minimal and most likely to impact a single storm, usually closer to the US in the Gulf, Caribbean, or W. Atlantic. Ironically, these are also where the water is warmer to deeper levels ni the ocean, mitigating those impacts. But, a good case is Isabel in 2003 -- as it passed over the waters that Fabian had churned up just a week prior, the storm rapidly began its weakening process, as the master's work of one of my friends has shown.

Do note that the waters off of tge coast of Africa are generally warm only near the top, due to the cool Canary current running through the area, but that since storms are generally pretty weak out there, any such impacts are usually quickly relieved.

So, in summary, it's possible -- and has happened before -- but not too likely.