No, the RMS rating determines how much wattage (volume) a speaker can handle before blowing out. Generally, this just means a more powerful magnet and a cone with a center sleeve which is longer and a more durable cone. In fact, in some scenarios, the speaker cone could be constructed out of materials which are more durable, but have less desirable sound properties.
In fact, this can be easily illustrated by the fact that no matter the RMS rating, you will still want to purchase tweeters and bass to produce the full range of sound. Were higher RMS directly correlated to sound quality, you would not need to buy these at the high end - but this just isn't the case.
If you don't need to simulate the volume of a jet plane at 5 feet from the engine and aren't planning to blow out your eardrums, lower RMS ratings are fine. You will probably want your peak volume to be about half to two thirds of the RMS rating. At the high end of the rating, speakers tend to resonate and generate bad sounds.
Instead, what you should look for are speakers made of quality construction and quality materials. For example, low end tweeters tend to be made of silk and high end tweeters made of titanium. Speaker cabinets (these are probably the most underrated aspect of sound quality) should be correctly ported, be made of quality materials and construction and have a mathematically correct resonance chamber to ensure that sound off of the back of a speak is properly delayed and the sound coming out has a good resonance.
Good speakers will also have a high amount of directivity. This means that sounds should be heard while standing in the broadcast field for the speakers while not heard outside of the broadcast field. Speakers with a high amount of directivity will have a markedly pronounced volume difference when you move out of the broadcast field. The higher the differential, the better the directivity. This is generally achieved by setting tweeters back into a horn within the cabinet rather than being flush-mounted to the surface of the cabinet. This prevents sounds from bouncing off of surfaces which alter the sounds and deteriorate sound quality.
There is also something to be said for speaker size. Generally, with mid-range speakers, I have found that larger speakers produce better sound. They have more surface area to generate a richer sound. This does not translate well to bass speakers however as 10-inch bass speakers produce a tighter hitting sound while 12-inch bass speakers produce a richer and deeper more resonating sound. If you listen to music with a lot of emphasis on drums, you will probably be happier with 10-inch bass speakers, while music with more bass guitar is better suited to 12-inch speakers. Or, you may with to simply get one of each.
Similarly, your receiver can play a big part. You want to ensure that it does a good job of filtering the hertz ranges. Trying to play bass sounds out of your tweeter will shorten the life of your tweeter and sound terrible. The better a receiver can divide the spectrum and send it to the correct speaker, the better your sound system will sound.
(I sold home theater equipment on commission for about 2 years)