The way the small engine throttle works is by a spring and vane system. The spring pulls on the throttle to increase engine speed. The vane is there to catch the air flow coming off of the engine fan and counteracts the force of the spring. These two actions create a balancing act which keeps the engine running at the desired speed. As the engine speeds up, the air from the fan blows harder, which pushes the vane. As the engine slows down, the spring is allowed to pull harder on the throttle.
If you are looking to increase the running speed of the engine, the easiest way to accomplish this is to extend the mounting point of the spring, which allows it to pull harder against the throttle and the vane.
If you attach a string (or something else to pull up the slack a little more), you'll set the lower limit of travel as to where the engine will run at. If the engine were under a bunch of load and slowed down, the throttle plate in the carb would open up to allow more air in. I think your idea would work fairly well, with minor drawbacks, but it would also be dependent upon the end goal (if you want it to run faster or what).
I have a Craftsman lawnmower with a B&S engine on it. One of the front fairings had broken off and exposed the area just above the carburetor where the spring resides. Through running it around the yard, the mounting point of the spring was bumped which effectively shortened the space between it and where the spring attached to the throttle mechanism. It began to run slower as a result and didn't have the same power output. I realized what the problem was and pulled the mounting piece back further, which not only fixed the issue, but actually allowed the engine to run a little bit faster. I think if your ultimate goal is to run the engine a little stronger, remounting the spring further away or spacing the spring out a little further would be a better option, but that would just be my opinion.