They can, provided they hold at least half the ownership and the real decision-making authority over pricing, staffing, spending and the manager's own employment. A hired manager is a normal feature of a hospitality business; what E-2 excludes is a passive owner who has delegated control.
Control is shown by who decides, not by who is on site every day
The consular standard asks whether the applicant is in a position to develop and direct the enterprise, and treats ownership of at least fifty percent, or operational control through a managerial position or other corporate device, as ordinarily sufficient. Keeping a manager does not defeat that, but the documents must show the couple's authority. The operating agreement should reserve major decisions to the owners; the manager's contract should make clear he reports to them and can be replaced by them; and the business plan should describe what each spouse does—one on guest operations and the restaurant, the other on bookkeeping and capital projects, for example.
What the officer will not accept is an investment in which the couple provide money and the manager runs the inn under his own discretion, because that describes a passive investment rather than a treaty investor. The remaining conditions, from treaty nationality and a substantial at-risk investment to a non-marginal enterprise, are assessed alongside control.