Yes, raising clip leans mixture, lowering clip enriches, by changing position of needle in main jet. But this only applies to conditions from say 1,500 rpms on up, not low speed. The low speed is dialed in by pilot jet size, the smaller of the 2 jets, and by fuel mixture screw. The reason low speed is relatively unaffected by needle clip position is that needle is tapered twice & extremely close tolerance at initial opening of same. A few thousandths of needle rise in needle jet and even less increase in actual clearance, as flow, through that jet that needle rides in causes little change at low speed, with flow through idle/pilot jet being the main influence on low speed running.

As I mentioned in several Carburetor threads the idle to midrange characteristics are adjusted with the fuel mixture screw. From this base setting the fuel/air flow through carb transitions into higher speed via the slide piston movement, opening to allow more air, and needle position, opening to allow more fuel. If it's too lean at base setting of idle/pilot jet mixture then it's an uphill battle to make power. If too rich then it takes power away as engine fights to run at over-rich until speed & momentum pick up to consume that extra fuel while imbalanced.

There's more than one way to adjust fuel mixture screw, mentioned in other threads. You can open fuel mixture screw to highest smooth idle speed & then adjust idle speed with slide piston stop screw on side of carb. This is called best rich idle.

Or you can open fuel mixture screw to highest smooth idle speed, then close until engine speed just drops, counting number of turns from highest smooth idle to point of engine speed drop. From that point back it back out 1/2 way between the two points. Some call this best neutral idle speed.

Or, you can leave it at that point at which engine idle speed just began to drop, which is called best lean idle.

If slide piston's needle is adjusted by needle clip position to the rich side then idle mixture has to be adjusted to transition properly, with same being true of a lean clip position. From a lean clip position trying to transition from a rich idle is going to cause a bog or loss of power: too much air in mixture. From a rich clip position, trying to transition from a rich idle is going to flood too much fuel in, causing bog or stumble. From a medium position of both the transition is smoothest, with no bog or stumble.

Every engine/carb combo is different, and spark advance, compression, wear and several other factors effect what is BEST for your engine. Because of low vacuum pressures at intake and low compression, vacuum leaks don't show up as violently as in large multi-cylinder engines. Therefore an integral part of carb/engine setup is assuming an intake leak & testing for it. Again, playing the unlit gas jet from a propane torch around intake manifold & carb is best to reveal intake leaks. Second best and messier is to spray WD40 around all sealing surfaces between cylinder head & carburetor, and with either method if engine speeds up at all you have an intake leak.

Engine/carb cannot draw fuel other than by vacuum principles, which are magnified through the jet & air circuits in carb. These cannot function unless properly cleaned with solvent & jet wires, and further cleaning after jet wires with more solvent spray & then best to follow with high pressure air.

The fuel/air intake functions cannot take place properly unless the valves are adjusted & timed correctly, to take advantage of the piston dropping in cylinder, causing the negative inlet vacuum pressures, which draws fuel & air through carb. None of the valve function can properly occur unless camshaft is properly indexed to piston position at Top Dead Center. Proper intake valve opening, which causes intake vacuum to draw in air/fuel mixture, won't occur unless valve lash/clearance is adjusted properly. With all of those in proper adjustment nothing can work correctly unless spark event is properly timed to piston position & valve opening, relative to Top Dead Center, to occur at optimum point of piston travel in cylinder.

Spark event cannot be properly timed [advance/retard points plate] unless points gap is adjusted as well, because points gap adjustment effects dwell angle, of when spark actually occurs and for how long. The points gap has an effect on when points open and how intense the spark generated by coil is at plug. Proper plug heat range and type of plug & type of plug connector also effects spark intensity & every power pulse of engine.

One would see that these are relatively tiny engines with miniscule power output. On a multi-cylinder 100-500 hp engine a small error might cause a 10% loss of power but there's plenty more available. On a tiny little engine fighting to make 7 hp a small error can result in a much larger proportional loss of power, because there's no reserve, and no extra power to mask the deficit loss.

Ballpark or sloppy, inaccurate adjustments are a bad start if we want to enjoy all that the little engine can offer, which is an amazing lot of pleasure. Extremely precise adjustments & meticulous attention to details & using the best components you can afford gives large returns on the investment of time, labor & materials. Just as well, initial setup of the whole engine in all aspects of cam/valves, air/fuel intake mixture, battery/electrical/ignition/spark & grounding etc. is the only way to get where a guy or gal really wants to be.