Around a circuit, the EMF is non-conservative. In fact, we are in a closed loop and "its" work (the EMF is actually the work itself per unit charge) is non-zero (contrarily to conservative forces/fields...). However, in general the EMF (not motional) does not act around the whole circuit, but only on a part of it.

* **How do we see that EMF is not conservative?**

Edit 17/01/'20: Let me explain a little more my point. EMF is *defined* around the whole closed circuit. However, if we have a battery, we know the EMF acts within that battery only. The *force* which moves the charges inside the battery (or whatever) does not generate a vector field in the surroundings, as Newton or Coulomb's forces. If we had a vector field through all the circuit, then we could say 'hey, that's due to a non-conservative force since the work on the closed path is non zero'. But instead we don't have such a field; it may be similar to assuming gravity is working on a closed square path only at *one side* of such path, while at the other sides gravity is switched off and the travelling particles are moved by another external force. Well, the work due to gravity is non zero all over the path, nevertheless Newton's force is conservative. 

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About motional Emf:

* **Why motional EMF is not localized on the circuit?**