Will I have a signal while hiking the La Soufrière volcano or in the jungle?

Yes, in most areas. You will have a strong signal at the base and in the main town of Basse-Terre. While hiking the La Soufrière volcano, the signal is surprisingly good on the trail but may drop at the summit due to weather/clouds. You will have a signal at all major beaches and towns, but expect "dead zones" if you go into the deep interior of the National Park.