It really depends. Not all pulmonary embolisms are emergent conditions, and depending on the circumstances (recent surgery or high risk of bleeding? Saddle emboli? Etc.), may be just monitored for a few days before getting fibrolytics or high power anticoagulants. However, they can easily turn into emergency conditions. Additionally, yes, the "EMS classic" presentation of profound hypotension, chest pain, hemoptysis, and hypoxia not fixed by supplemental oxygen are not served well by EMS waiting around on scene.