Yes, I think that you could do that, but would you really want to? What if a Realtor that you really don't like, or is just not that good of an agent happens to have a buyer that buys your house. Now you are stuck with using that Realtor to find and purchase a home. I wouldn't want to be locked in to using an agent that might not be my choice.

I agree with Terriks, I wouldn't want to sign an agreement with any old agent.
The agent that brings a buyer already wants that buyer to buy, the best you can do is price your house well, keep it looking good.

Since I am of the opinion that buyer's agents are not that important if you know what you want, I say go for it. But then again I always use a buyer's agent that gives me cash back at closing.

I did 3% to buyer's agents when the standard around here is 2.4%. We were FSBO so I thought it fair to offer a bit more for the hassle of dealing with us amateurs. It was an unusual house and sold fairly well I thought. The house went on the market 6 months later and sold in twice the time and at 10% less price in a relatively stable market.