Yes, if a licensed engineer, architect or certified cost estimator prepares it on unit costs (not a lump sum), certifies it matches the agreed damage, and it is detailed and reasonable. When FEMA writes the estimate for a large permanent work site less than 90 percent complete, it uses the Cost Estimating Format (CEF). Either way, FEMA reduces the estimate for actual or expected insurance proceeds.
A unit-cost estimate signed by a licensed professional engineer, licensed architect or certified professional cost estimator, with a certification that it was prepared to industry standards and corresponds directly to repairing the agreed damage; the current design or construction phase and known costs; actual costs for work already done; and your insurance policies and any proceeds.
A lump-sum estimate is the quickest way to have yours rejected. Build in foreseeable contingencies such as security and staging, because FEMA judges reasonableness line by line under the Chapter 6 reasonable cost rules.