If a contractor has not signed the Government contract award but has been performing services, does that legally bind the contractor to that Government contract?
Based on the information provided; there is no simple yes or no answer. A binding contract may or may not have been formed. Because the question was asked, I will assume there is some reason the government is hoping or trying to determine no contract exists.
If the government does wish for there to be a binding contract with this contractor and all the selecting a source rules and competition requirements were followed; just have them sign it already and be done with the concern/issue.
Back to the answer. "Contract formation" is fascinating and there is much case law and board decisions on this legal topic. We try to avoid it getting this far as much as possible in government contracting and why a definition of a contract exists at FAR 2.101. It includes phrase such as "unless otherwise authorized, are in writing..." and "becomes effective by written acceptance or performance...". You should take a close look at this definition and if your scenario is one in where performance alone might constitute acceptance. In summary:
1) If you were using simplified acquisition procedures (SAP) and received a quote... if the supplier has proceeded with the work to the point where substantial performance has occurred, the answer could definitely be "yes"; see FAR 13.004(b).
2) If this was a letter contract, a BOA, or other agreement and the express (in writing) terms indicate acceptance occurs with performance; then again "yes" possibly.
3) If you were using other than SAP; then the answer is the classic "it depends" as there are no additional FAR or Agency Supplement citations to cling to. Therefore, we recommend you contact your contracting attorney/legal staff ASAP. The principles of "contract formation" come into play and those are based on Common Law and the Uniform Commercial Code decisions, principles, and rules.
In general, in order for a contract to be formed and binding to both parties, there needs to be six essential elements: mutual assent (offer and acceptance), consideration, capacity, lawful purpose, certainty of terms, and a form provided by law. All of the facts and conduct of the parties must be considered and analyzed. Concepts such as apparent, implied, and/or actual authority need to be looked at as well.
Finally, a simple search in the AAP system would have revealed many very similar questions previously asked and answered. We remind and encourage you to search before submitting a question; it very well could save you a substantial amount of time.