If different domain has Exchange Server is SMTP needed in the Farm?

Hello Community

    There are 2 domains on the network DomainX and DomainY.

    DomainX has 12 domain controllers and numerous member servers, 
atleast one of the servers are hosting Exchange Server  and atleast one
server is running DNS.

    DomainY is a SharePoint 2010 Server farm.

    DomainX and DomainY have a trust relationship.

    Since there is an Exchange Server running in DomainX does DomainY
need to have SMTP or Exchange Server running in its domain to send and
receive emails?

    Thank you
    Shabeaut