RoC and Stability of a Rectangular Signal
Note that for $s\to 0$, the transfer function $H(s)$ doesn't have a pole because also the numerator approaches zero. In fact, you have
$$\lim_{s\to 0}H(s)=2\tag{1}$$
The ROC is the whole $s$-plane, except for $\textrm{Re}(s)\to -\infty$.