Measuring dispersion in circular data stats noob here.
I have a (circular) dataset with values in [0, 2pi]. I need some kind of a measure of how disperse or diverse the dataset is. I have looked a bit into non circular (regular) data, and I happened to come across coefficient of variation as a non-dimensional measure of dispersion in a dataset.
My question is: can I modify the coefficient of variation in my case as (circular stddev) / (circular mean) and use it as a dispersion measure?

I don't think this directly answers your question but you seem to be looking for a way to measure dispersion in circular data. As others have pointed out, there is a literature on circular statistics and standard solutions to this problem. The basic summary statistic for circular (or otherwise cyclic) data is the mean vector.
Assuming your data is not weighted, you interpret every angle $\theta_i$ as a unit vector.
$$ \bar{v}_i = [\text{cos}(\theta_i), \text{sin}(\theta_i)]$$
Your mean is then given by:
$$ \bar{r} = \frac{1}{n}\sum_{n} \bar{v}_i $$
The angle of $\bar{r}$ ($\theta_\bar{r} = \text{atan2}(y_\bar{r}, x_\bar{r}$) gives you the mean angle of the data. The magnitude of $\bar{r}$ ($|\bar{r}| = \sqrt{x^2 + y^2}$) ranges from 0 (data is completely dispersed, uniform) to 1 (all data points are identical). Circular standard deviation and angular deviation can both be computed from $|\bar{r}|$.
There are also a number of tests on dispersion, the most basic of which is the Rayleigh test (is the data sufficiently concentrated in a particular direction or not).
If you're a stats noob (like me) I would recommend something like Batschelet (1981), Circular Statistics in Biology. It gives a very easy introduction which explains why circular and linear measures should not generally be mixed and then provides a 'cookbook' of different tests and the assumptions which must be satisfied in order for them to be valid.
