Yes, if the agreement binds him to close on visa approval and the price is in escrow, releasable only on that condition. A letter of intent or a refundable deposit is not an irrevocable commitment and will not support the application.
Conditional closing is allowed; optional closing is not
Hypothetical example: The requirement that funds be at risk is often misread as requiring the buyer to close first and apply second. That is not the rule. Consular guidance accepts a purchase where the entire price is in escrow and the only condition of release is issuance of the E-2 visa, because the buyer has surrendered control of the money and is legally bound to complete.
What fails is anything that lets Dwayne walk away: a letter of intent, a deposit he can recover for reasons other than visa refusal, or a financing condition that has not been satisfied. The purchase agreement should therefore state that the buyer's sole condition is E-2 issuance, set a closing date shortly after approval and provide for the escrow agent to release funds on presentation of the visa. His lawyer on the U.S.
side and his immigration adviser should read the same draft, because a clause written to protect him commercially may be exactly the clause that undermines the visa.