Is cashing a check for insurance restoration work an agreement for payment complete on the project.

The answer to this is "it depends." If you have billed for the work and have performed the work then you can deposit it, pay your subs and suppliers, and move forward. It does not matter where the check came from. One caveat is that if the balance due is disputed (for instance you finish and they try and short pay you), and they put something like "Full and Final Payment" on the memo line, cashing the check will be considered "Accord and Satisfaction" and will later be considered by the Virginia courts as a full and final payment of a disputed debt.