Does the drain go directly into the floor under your sink? If so, you're O.K.
If you're saying that the drain goes into your wall and then runs under the floor, then you will have to lower it.
By the way, you can minmize the damage if you are lucky enough to be able to get to the pipes in the wall by pulling out your dishwasher. If so, you can patch the hole with drywall behind your dishwasher without having to float and paint the patch.
The rubber pipe couplings with hose clamps work well for this type of job, particularly when joining PVC to iron pipe.