Is it possible to manage an encrypted dataset for face recognition?
If I understand correctly, the setting describe by you is that you want to simulate a scenario where an encrypted dataset is hosted on an untrusted server, then a user can send encrypted image to it, the server blindly match the image with every encrypted image in the set, then return the user the best match. This seems not possible (at least without some carefully thought and design) because the server does not have the private key thus would not know which one is the best match. Of course the server can, for each encrypted image, return a result and the user can decrypt, then the user decide which one is the best match.

Whether the matching can be done in the encrypted domain depends much on what matching algorithm you use. Paillier is only additively homomorphic, meaning that you cannot do multiplication in the encrypted domain (except multiply a constant). The computation is restricted to an integer group, not real numbers. All of those constraints would restrict your choices, possibly only to those simple ones.