Before attempting to answer this question, it should be noted that your question is asking in part about cost reimbursement subcontracts. The FAR references given (4.804-1(a) and 52.216-7(d)) pertain to contracts between the prime contractor and the Government and may not necessarily pertain to the contract between the prime contractor and a sub-contractor. This is worth mentioning since the Government does not have privy of contract with subcontractors.
Assuming we are discussing a contract between the Government and a prime contractor, the answer to this question will depend also on your agency's regulations, whether or not FAR Clause 52.216-7 (as referenced in your question background) is included in your contract, and whether or not the conditions under FAR Part 42.7 have been satisfied. First, FAR Part 4.804-1(a)(1) states that files for contracts using SAT procedures should be considered closed when CO/KO receives evidence of receipt of property and final payment, unless otherwise specified by agency regulations. So in addition to the FAR requirements outlined in FAR Part 4.804-1(a)(1), the CO/KO must also comply with agency regulations, i.e., FAR Supplement, policy letters, etc. Second, assuming FAR Clause 52.216.7 applies, subparagraph (d) "Final Indirect Cost Rates" states that final indirect rates shall be established IAW Subpart 42.7 and subparagraph (f) "Quick-Closeout Procedures" states that these procedures are applicable when conditions of FAR 42.708(a) are satisfied. Lastly and in order to make a proper decision regarding this matter (question), the CO/KO will have to not only follow FAR Part 4.804-1(a)(1) but also agency regulations along with possibly FAR Parts 52.216-7 (d) and (f) and 42.7, specifically, 42.708.
Since we do not have all of the facts particular to your contract, program, and situation, we highly recommend that you consult with your KO/CO and Legal Office for further guidance.