Yes, why not. Key generation (including key generation for ECDH) and private key operations are relatively efficient compared to other cryptosystems such as RSA.
There are some things to keep in mind:
- standard ECC operations such as ECDSA do require a good random number generator to be present (this can be avoided by using deterministic signature schemes such as described in RFC 6979;
- the small key size makes it relatively simple to use quantum computers to break the system (calculations on smaller number mean less qubits required).
RSA keys of the same strength are only 4 times harder to crack on a QC if current research is any indication. That may not be much of a difference when push comes to shove.
Note that although ECC is relatively efficient compared to RSA, it still requires a fast (Montgomery) multiplier. On smart cards this is usually implemented in hardware - and with good reason. Compared with symmetric crypto, it's still a dog; doing 256 bit modular exponentiation on a 8 bit processor may take - ahem - some time to complete.
You might also require side channel attack protection as well.