The odds of the agent holding the house open and actually writing the contract for the buyers is very low. Although one of my listings was sold in December, by another real estate agent, who's client looked at it during my open house. In today's market, I feel you need to utilize every avenue available, to get the buyers to look at your home.
Open houses are a great way for real estate agents to meet new buyers and get their contact information. I believe that having a large number of buyer contacts, is also valuable to the sellers.
I understand that you want to keep your new carpet looking great - You may want to offer the people looking at your home disposable booties that slip over their shoes.