How feasible is it to perform pose estimation on a Raspberry Pi 4 using a Pi-Cam? I want to estimate hand poses and recognize gestures using an open-source library like OpenPose on live video. Considering the fact that such libraries are very computationally intensive. 

How likely is it that it will run on a Raspberry Pi 4 using a Pi-Cam while giving me something above 15 fps? Assume that the models are pre-trained.
If using TFLite python API, you may reach to 1/2 FPS. On downscaled custom Pose architectures you may get more FPS. You can try the TFLite c++ API as well, it might be a bit faster than the python one. 
To reach more than this you would need a TPU or a library that could use GPU computation of the Pi. Nevertheless, I doubt that it would reach 15 FPS with OpenPose open-source library.