Hi,
I am not sure why your business allow SE from Contract. As you have contract you to create PO from contract and later create SES from PO.
Yes, with development you can achieve enter cost center and also control on t.code ML90 for SES screen where you can link department with cost center (KS02) and link G/L account with cost center with company code in t.code OKB9.
Regards,
Biju K