Is it possible to achieve activity recognition on a single image?
The short answer, yes and even with a good performance, although not with same accuracy as with multiple frames.
There are actually many different architectures that rely on classifying each single frame as part of their process (you can treat the overall model as an ensemble-model of multiple frames).

There is a great article by "Schindler et al."  about exactly this question:

Action Snippets: How many frames does human action recognition require?