Can we export SID's to new domain control?

Yes we can export SID's to new a DC

SID is unique for each object, so when you migrate user into another domain, its SID is assigned from that domain SID's database and it's also unique within that domain. The only difference for existing user in the domain is that SID History is set up with SID from previous domain to preserve access to network resources without changing ACLs on files/folders by administrator.

Yes, we can export the SID to new DC.

This can be achieve using ADMT tool