Check out Conservation Drones - https://conservationdrones.org/ and Serge_Wich's research. Also Serge's (and Lian Pin Koh) book is great - Wich, S.A. and Koh, L.P., 2018. Conservation drones: mapping and monitoring biodiversity. Oxford University Press.
Here is a recent special on using drones for biodiversity purposes with some relevant references: Article Editorial of Special Issue “Drones for Biodiversity Conserva...
The use of drones in biodiversity-related research include: the application of LiDAR (see Kellner, J.R., Armston, J., Birrer, M., Cushman, K.C., Duncanson, L., Eck, C., Falleger, C., Imbach, B., Král, K., Krůček, M. and Trochta, J., 2019. New opportunities for forest remote sensing through ultra-high-density drone lidar. Surveys in Geophysics, pp.1-19.); photogrammetry; seed dispersal, seed detection (using object recognition algorithms - see Buters, T., Belton, D. and Cross, A., 2019. Seed and Seedling Detection Using Unmanned Aerial Vehicles and Automated Image Classification in the Monitoring of Ecological Recovery. Drones, 3(3), p.53.); canopy height modelling (see Mohan, M., Silva, C., Klauberg, C., Jat, P., Catts, G., Cardil, A., Hudak, A. and Dia, M., 2017. Individual tree detection from unmanned aerial vehicle (UAV) derived canopy height model in an open canopy mixed conifer forest. Forests, 8(9), p.340.); water sample collection (see Article Can drones be used to conduct water sampling in aquatic envi...
); and image analysis for monitoring (see Tait, L., Bind, J., Charan-Dixon, H., Hawes, I., Pirker, J. and Schiel, D., 2019. Unmanned Aerial Vehicles (UAVs) for Monitoring Macroalgal Biodiversity: Comparison of RGB and Multispectral Imaging Sensors for Biodiversity Assessments. Remote Sensing, 11(19), p.2332.).
The potential for innovation and application in the field is huge - limited by our imagination, policy, cost and methodological ambiguity.
Yes, it is possible to study at least some aspects of biodiversity with drones. But it depends on what taxon are you talking about: Fish, plants, mammals etc.
Here is some additional information:
Article Drones for Conservation in Protected Areas: Present and Future
Article A low-cost drone based application for identifying and mappi...
Article The social implications of using drones for biodiversity conservation
There are also research groups/companies delivering services on that:
We, Reef Guardians Hawaii, are currently deploying aerial and underwater drones in a program called "Robots on the Reef" to study the health of coral and fish populations. This is new technology and the gathering of data in high resolution at regular intervals and repetitive paths of surveillance has been accomplished. The next phase remains in the AI realm with the interpretation of the data and an end goal of doing it in near real time. In conclusion drones are a very viable technology for studies in bio-diversity. One working example is the ability right now of shark species recognition from commercially available aerial drones. This research is progressing both in Australia and in Santa Barbara,CA at UCSB's McCauley Laband through Reef Guardians Hawaii programs.