The run up can be performed while "plowing." Plowing is a method of taxing a seaplane that produces a lot of water drag on the floats--basically its a tail low position. The pilot can further encourage this nose high attitude by applying full back pressure (up elevator). This accomplishes increasing drag on back of floats and keeping the nose as high in the air as possible, because water can do serious damage to a propeller at high RPM.
According to the FAA's Seaplane manual FAA-H-8083-23 (Ch4 p.4-12):
"All checks are performed as the seaplane taxies, including the engine runup. Hold the elevator control all the way back throughout the runup to minimize spray around the propeller."
SIDENOTE: I'd like to add that when I did my seaplane training, my instructor (who also owned the airplane) did not like to do it this way because he said plowing doesn't provide adequate engine cooling due to nose high attitude and relatively slow speed. He preferred to do the run up "on the step." Which is a different method for taxing at high speed when aircraft is hydroplaning on the "step", which is the part of the float that goes from the fat front part to the skinner back part.
