Is this block encryption scheme using PCBC for RSA secure?
Is there any issue resulting from using that with RSA instead of a symmetric cipher?


The difference - with regards to security - between symmetric and asymmetric encryption is that anybody is supposed to have the public key for asymmetric encryption, including the attacker. This has to be taken into account when generating a mode of operation for RSA.


  Assuming that RSA is as secure as BlockCipher XYZ, will this give the same security as PCBC used with XYZ?


Nope. Assume that the first plaintext block is zero. Then the IV (initial chaining value) is encrypted twice in this scheme. As modular exponentiation itself is deterministic, this will result in repetition within the ciphertext. This repetition will show that the plaintext block is zero, thus leaking information to an attacker.

That's a fundamental break in CPA security. There may be other issues, but this is enough to declare the scheme to be broken when used as direct replacement of CBC or PCBC with a symmetric cipher.