Not necessarily. It depends on an offsetting play between amount of noise (variance) and slope steepness: steep slope with lots of noise might return lower correlation coefficient than a shallow slope with less noise. If noise is the same, the relation showing a steeper slope will also show a stronger correlation.
The correlation is a measure for the extent of linear dependency between two variables, not for the slope of a line. In other words, it says how much a relation between two variables is linear, not what the linear relationship actually looks like. If variables $y$ and $x$ are related by an equation of the form $y = a+bx$ with $b\ne0$, then $corr(y,x)=1$ if $b>0$ and $corr(y,x)=-1$ if $b<0$. Nothing is stated about the slope $b$, hence even the slightest slope will lead to a correlation of 1 in absolute value (on a population level)
However, with random variables, noise comes into play so that even if a relation is perfectly linear it gets 'blurred' and thus the linear dependency is not so easy to determine anymore: $y = a+bx + \varepsilon$ with $\varepsilon \sim (0,\sigma^2)$. This leads to correlation coefficients unequal to 1 in absolute value. If there are only few observations, a shallow slope $b$ might get overwhelmed by this noise, causing the linear relation to not show at all and lead to a very small correlation coefficient. A steeper slope has less chance of getting 'overwhelmed' and thus the correlation coefficient may be higher. In a world where there's lots of data points ($n \to \infty$) the correlation will approach its 'true' value, independent of the slope. But it could very well be the case that $y$ and $x$ have a shallow slope and little noise, making the linear relationship clear, while $y$ and $z$ (where $z$ is any other random variable) have a steep slope but lots of noise, making the linear relationship not so certain.
This coincidentally shows the limitations of using correlation coefficients to model relationships between multiple variables and why regression is more useful in that case. As @Paze pointed out, hypothesis testing is used to test for significance of the (regression and if needed, correlation) coefficients.
[if needed I could eventually (?) provide a graphical illustration]