No, if you use a contracted-for relocation service that is a substitute for reimbursable relocation allowance, you will not be reimbursed for the relocation as well.
Code of Federal Regulations
Effective Date Note:
By FTR Amdt. 2011-01, 76 FR 18343, Apr. 1, 2011, § 302-12.5 was redesignated as § 302-12.6, effective Aug. 1, 2011.