Yes, of course. if you don't specify CKA_TOKEN=true the private key is not loaded in the token by it is loaded as temporary, session object.
I was reading the PKCS#11 specification again. I read the following about RSA Private Keys:
"Table 36: RSA Private Key Attribute:
CKA_MODULUS, Big integer Modulus n
CKA_PUBLIC_EXPONENT Big integer Public exponent e
CKA_PRIVATE_EXPONENT Big integer Private exponent d
CKA_PRIME_1 Big integer Prime p
CKA_PRIME_2 Big integer Prime q
CKA_EXPONENT_1 Big integer Private exponent d modulo p-1
CKA_EXPONENT_2 Big integer Private exponent d modulo q-1
CKA_COEFFICIENT Big integer CRT coefficient q-1 mod p
Tokens vary in what they actually store for RSA private keys. Some tokens store all of the above attributes, which can assist in performing rapid RSA computations. Other tokens might store only the CKA_MODULUS and CKA_PRIVATE_EXPONENT values. Because of this, Cryptoki is flexible in dealing with RSA private key objects. When a token generates an RSA private key, it stores whichever of the fields in Table 36 it keeps track of. Later, if an application asks for the values of the key’s various attributes, Cryptoki supplies values only for attributes whose values it can obtain (i.e., if Cryptoki is asked for the value of an attribute it cannot obtain, the request fails). Note that a Cryptoki implementation may or may not be able and/or willing to supply various attributes of RSA private keys which are not actually stored on the token. E.g., if a particular token stores values only for the CKA_PRIVATE_EXPONENT, CKA_PRIME_1, and CKA_PRIME_2 attributes, then Cryptoki is certainly able to report values for all the attributes above (since they can all be computed efficiently from these three values). However, a Cryptoki implementation may or may not actually do this extra computation. The only attributes from Table 36 for which a Cryptoki implementation is required to be able to return values are CKA_MODULUS and CKA_PRIVATE_EXPONENT.
If an RSA private key object is created on a token, and more attributes from Table 36 are supplied to the object creation call than are supported by the token, the extra attributes are likely to be thrown away.
If an attempt is made to create an RSA private key object on a token with insufficient attributes for that particular token, then the object creation
call fails and returns CKR_TEMPLATE_INCOMPLETE."
This means that you should try with different sets of attributes.
For example try to remove CKA_PUBLIC_EXPONENT