Afsal, skimmers are designed by the manufacturers to handle a certain amount of water per hour - generally 1 to 1 and a half times their capacity. In other words a 250l skimmer should be receiving 250L to 375L per hour in order for them to work effeciently. Push anymore water through the skimmer and you won't be getting optimum performance.
So the short answer is no, it wont work harder, it will continue to work at the rate it was designed for, but you will be underskimming your system.
Generally these ratings are for less that what the skimmer can handle anyway and the rule of thumb is to go for a skimmer that is rated for more than your system volume.
HTH