If we used
Cipher.getInstance("AES/CBC/NoPadding"), will it be vulnerable to padding oracle attacks?
If there is no padding then the cipher is not vulnerable to padding oracle attacks that originate from the cipher implementation. The cipher expects full blocks of ciphertext and simply decrypts them to whatever information, even if that seems random.
However, padding oracle attacks are part of a larger set of attacks called plaintext oracles. Plaintext oracles react to information that is released by an implementation when the plaintext is altered. As CBC doesn't provide message integrity the attacker can perform any kind of change.
The most simple example is if the code itself pads / unpads the message using e.g. PKCS#7 padding. In that case, the padding oracle is not present in the cipher, but present in the code surrounding the cipher. It would be just as bad as a padding oracle attack that was created by using the cipher implementation.
Another, less obvious examples of plaintext oracles are the attacks on the XML-encryption standard. Those are at least as efficient as padding oracle attacks.
Of course, as always, the plaintext oracle must need to be present; for instance, local file encryption may not expose an online oracle. And as always, plaintext oracles are best avoided by adding a message authentication tag for message integrity (such as a HMAC calculation over the IV and message, or by using an authenticated / AEAD cipher such as GCM).