If I request my identity certificate to be revoked for any reason other than key compromise, would the private key also be revoked in result?
There is no revocation of different parts of the certificate, i.e. a certificate is either revoked in full or not revoked at all. This also means that the certificate itself is revoked and not the key of the certificate, i.e. other certificates which use the same key are not affected by the revocation. And this means that you are free to reuse the key for another certificate.