Not quite. What happens with any weather is the following.
1.If an existing weather such as Rain is up and you switch in your Groudon with Drought, the weather will change to Sun. This works the same for any weather.
2.If two Pokemon with a weather summoning ability switch in on the same turn e.g Groudon and Kyogre, the slower Pokemon's weather will be up. So if Groudon was slower than Kyogre, Sun would be set up.
Weather can be overpowered by the means of moves like Hail and Sunny Day also.