Are (empirical) Rademacher complexity always positive?
Yes, the empirical Rademacher complexity is non-negative, and this follows from Jensen's inequality. 

For completeness, the empirical Rademacher complexity $\hat{R}(\mathcal{F}, X)$ given a sample $X = \{x_1, \ldots, x_m\}$ and a class of real-valued functions $\mathcal{F}$ whose domain contains $X$ is 
$$
\hat{R}(\mathcal{F}, X) := \mathbb{E}_\sigma \sup_{f \in \mathcal{F}}\sum_{i = 1}^m{\sigma_i f(x_i)},
$$
where the expectation is over $m$ independent random variables $\sigma:= (\sigma_1, \ldots, \sigma_m)$ sampled uniformly from $\{-1, 1\}$.

Notice that $\sup_{f \in \mathcal{F}}\sum_{i = 1}^m{\sigma_i f(x_i)}$ is a convex function of $\sigma$, because it is the supremum of linear functions. Then, by Jensen and linearity of expectation,
$$
\mathbb{E}_\sigma \sup_{f \in \mathcal{F}}\sum_{i = 1}^m{\sigma_i f(x_i)} 
\geq \sup_{f \in \mathcal{F}}\sum_{i = 1}^m{\mathbb{E}[\sigma_i] f(x_i)}
= 0.
$$

The final equality follows because $\mathbb{E}[\sigma_i] = 0$ for all $i$.