Signing is expected; paying is the question. The purchase agreement can be signed and the funds placed in escrow with release conditioned on visa issuance, which shows commitment without losing the money if the visa is refused. Closing unconditionally before a decision puts the purchase price at risk.
Sequence signing, escrow and the interview
A common sequence is: sign the purchase and shareholder agreements with a visa condition; deposit the price into escrow under written release terms; apply for the visa with the signed agreements, escrow confirmation, funds trail and seller's financial records; attend the interview; and close on issuance. The seller receives the money at closing under this structure, but whether a six-week target is workable depends on document readiness and current interview availability; do not waive the condition merely to meet the target. If the seller refuses any condition, the applicant must decide whether to accept the risk of owning a US business he cannot enter to run; that is a commercial decision, not an immigration one.
Build in time for state licensing of the business under new ownership and for the transfer of contractor bonds, since a business that cannot legally operate on closing day is a weaker case. Check actual consular interview availability when planning.