The answer is probably not, and here's the explanation.

Check this out: https://puckpedia.com/salary-cap/buyouts. 

The main buyout window ends June 30, and the new contract does not become active until July 1. Therefore, the new contract could not be bought out in the first buyout window because it's not an active contract yet. However, teams can receive a second buyout, which is in July. At that point, the extension is an active contract, and if it met the second buyout criteria, it could be bought out.