As a general rule, no. When you perform a combat maneuver, you get what the maneuver explicitly gives you and that usually does not include damage.
There are some forms of attack that will automatically grant a combat maneuver for free, and there are probably some feats which let you do damage while doing the combat maneuver. But if you use your whip to disarm or to trip, it doesn't do any damage.
For reference:
PRD - Combat Maneuvers wrote:
Determine Success: If your attack roll equals or exceeds the CMD of the target, your maneuver is a success and has the listed effect. Some maneuvers, such as bull rush, have varying levels of success depending on how much your attack roll exceeds the target's CMD. Rolling a natural 20 while attempting a combat maneuver is always a success (except when attempting to escape from bonds), while rolling a natural 1 is always a failure.
Emphasis added.
When you look under the Trip maneuver, there is no call to roll for damage.
