Closing outright before the visa decision puts the full purchase price at risk if the visa is refused. The usual protection is an escrow that releases the balance on visa issuance. If the seller insists on closing, the couple should decide with eyes open, since a completed purchase is strong commitment evidence but offers no refund on refusal.
Escrow protects the buyer; closing proves commitment
Hypothetical example: the seller has another interested buyer and wants funds in hand within thirty days, well before the earliest consular appointment. The couple face a genuine trade-off. Completing the purchase demonstrates irrevocable commitment beyond argument and lets them start preparing the shop through a local manager, but if the E-2 visa is refused they own an Idaho business they cannot enter to run.
Escrow with release on visa issuance is the standard middle path, and many sellers accept it when the deposit is meaningful and the timeline is explained. A third route is to close but retain the seller under a short management contract until the couple arrive, which keeps the business trading and the evidence intact. Whatever structure is chosen, the couple must not enter the United States as visitors and begin operating the shop while waiting; running the business is E-2 work, and doing it without the visa would jeopardise the application.