Answer: The short answer is yes, but you need to understand why.
IRC 401(a) includes the exclusive benefit rule, which requires that a plan benefit employees of the sponsor. Because of other Code provisions (414(b), (c), (m), (n), or (o), 401(c), 7701(a)(20), etc.) people who are not actually employees of the sponsor can be treated as though they were, and thus satisfy the exclusive benefit rule. However, if you are not an employee or deemed to be an employee of the sponsor (or the beneficiary of a participant), then the plan cannot cover you.
So, let's ask if the owners of a business can be common law employees of a staffing firm. It doesn't matter whether the business is a sole proprietorship, corporation, LLC, partnership, or some other breed.
The answer is, almost invariably, no. The notion that a staffing firm is hiring, firing, exercising control, giving directions to what amounts to its own client is ludicrous. The staffing firm is functioning as little more than a bookkeeping service, and clearly is not the employer, all of its promotional literature to the contrary notwithstanding.
This was the opinion of the IRS and two courts in the mid '80s, when Professional and Executive Leasing's plan was disqualified for failure to satisfy the exclusive benefit rule. The logic of those opinions is very sound and very hard to dispute. Although I guess somewhere there might be an exception, I cannot imagine a case in which the staffing firm would be the employer of its client business's owners and hence could be the sponsor of a plan covering those owners.
Now, the LLC could certainly co-sponsor the plan with the staffing firm, and thereby get around the problem, but the staffing firm runs the risk of disqualification if it includes the owners in a plan it sponsors alone.
Now, let's ask the question you didn't ask. Can the staffing firm cover the rank and file employees? This depends more on the situation, but for the average staffing firm arrangement the answer is no. To be more specific, I have on my desk a thick notebook of paperwork generated by one of the nation's leading staffing firms, all of which says the firm is the true employer. I spent hours going through it, and came to the conclusion that once you clawed your way through the paperwork, the employer-employee relationship was still between the recipient and the worker, not the staffing firm and the worker. If that is true, then the staffing firm cannot cover the rank and file employees either, because they are not the common law employees of the firm. Getting a W-2 doesn't make you an employee of the person who gave it to you, any more than getting a 1099 makes you an independent contractor. Being regarded as the employer for payroll tax purposes does not make you the employer for qualified plan purposes.
Case after case after case has reaffirmed this.
These issues are discussed in more detail in Chapter 4 of my book, Who's the Employer?, if you'd like more information and specific citations.
In other words, I would be very worried about putting the employees into the staffing firm's plan, unless the LLC co-sponsors it.