Q:

Does X509Certificate2 specifiy key exchange algorithm?

Does X509Certificate2 class (or a certificate itself) specify the preferred/required key exchange algorithm (e.g. RSA or RSAES-OAEP) to be used for symmetric encryption?

A:

No, an X.509 certificate does not specify anything like that. Nor should it. 
The certificate only defines general use cases of the key (e.g. key encipherment). The choice of the right key exchange algorithm is however responsibility of the protocol, not the certificate itself.

Note that TLS specifications nowadays contain ECDHE_ and DHE_ ciphersuites. For this kind of protocol the private key is used to sign parameters for entity authentication rather than to directly encrypt a key. The messages themselves then use a symmetric cipher for encryption.
I presume however that your question was more about, for instance, Cryptographic Message Syntax encryption, XML encryption or other container formats.

