The answer is yes. There are various methods exist for sampling the zooplankton of a lake or pond. The most common method is to pull a fine mesh net through the water. This can be done either vertically or horizontally, and then collect the animals that have been retained by the net.
As zooplanktons mostly feed on phytoplanktons and phytoplanktons tend to remain close to water surface during daytime for sunlight availability, zooplanktons will also remain close to water surface for predation during daytime. You can compare daytime and nighttime sampling results and observe who are present or absent.
Zooplankton species exhibit phototactic movement, some groups are positively phototactic and some are negative. Night and day sampling of zooplankton from the same location will definitely help you to understand the difference.
Yes, you probably can, but the results will not be comparable with most studies. Zooplankton activity is strongly associated with daylight. Interesting test results could be obtained by comparing day and night samplings.
Depending on your study question, study site and species/size of zooplankton, the timing of sampling is incredibly important. These organisms are capable of intense diel vertical migrations - meaning that they may migrate in or out of the surface waters during the day or night.