It is workable but you have removed your own protection. An unconditional agreement obliges you to complete whether or not the application succeeds, which converts an immigration risk into a commercial one. Sequencing the deal and the application together is what avoids that.
Sequence the deal so a refusal is survivable
The usual structure protects both requirements at once: a purchase agreement whose completion is conditional on visa issuance, with funds held under escrow instructions that release irrevocably to the seller on closing, so the capital is genuinely committed while your exposure is defined. Hypothetical example: a buyer from Saint-Cyrille-de-Wendover signs an unconditional agreement for a New Hampshire fleet-graphics business closing in five weeks, then asks what the application will take; he now owns a business he may have to run through a manager or resell, and neither outcome was priced into the transaction. Where a deal is already signed, the questions are practical.
Can completion be deferred by agreement. Can a management arrangement operate the business lawfully in the interim without the buyer working in the United States. Is the capital position strong enough that a delay is only inconvenient.
The general lesson is that E-2 timing is driven by the documents you sign months earlier, not by the processing queue you join afterwards.