Supposedly, people of higher levels of intelligence do learn faster than people of lower levels of it. But this is an awfully coarse observation, and different people can learn at drastically different speeds in different environments.
A few quick points:
There is a massive empirical literature that shows that fairly strong correlations are obtained between IQ and important real world outcomes, perhaps most notably educational and job performance, often in the r = .5 range (see here for a summary).
Correlations with learning are complicated by what we mean by learning. In particular, if we define learning as the improvement in performance between two time points, then we have what is sometimes called a difference score or gain score. While this is an intuitive way to think about learning, gain scores often have slightly counter-intuitive properties. For example, on some tasks, gain may be negatively correlated with initial performance levels. This makes sense when you think that those who perform poorly initially often have more to learn. However, initial performance typically correlates well with final performance after a period of learning. As such, correlations of gain scores with ability can be a little strange also.
You might want to read some of Philip Ackerman's work on ability-performance correlations over practice.
There's some further discussion of the change score issue in learning here:
Ackerman, P. L. (1987). Individual differences in skill learning: An integration of psychometric and information processing perspectives. Psychological Bulletin, 102:3-27.