Not as a matter of immigration law, but the business must be lawfully operating, so someone must hold the licence. If a qualifying employee holds it, the buyer must still develop and direct the enterprise.
The licence question is about the business being real, not about the investor's trade
The E-2 rules do not require an investor to be licensed in the trade the business practises; they require a real, active commercial enterprise that the investor develops and directs. State contractor licensing is what makes an electrical business lawful to operate, and if the buyer cannot hold the licence at closing, the enterprise must have another qualifying individual who can, usually an employee, and the state board's rules on a change of ownership must be satisfied. That arrangement is compatible with E-2 as long as the buyer retains control of the business decisions, finances and direction while the licensed qualifier is responsible for the technical scope.
Explain the arrangement clearly in the business plan, including the buyer's own plan to sit the state examination. A file that is silent on licensing invites the officer to doubt whether the business can operate at all after closing.