Automatic pathological speech detection approaches yield promising results in identifying various pathologies. These approaches are typically designed and evaluated for phonetically-controlled speech scenarios, where speakers are prompted to articulate identical phonetic content. While gathering controlled speech recordings can be laborious, spontaneous speech can be conveniently acquired as potential patients navigate their daily routines. Further, spontaneous speech can be valuable in detecting subtle and abstract cues of pathological speech. Nonetheless, the efficacy of automatic pathological speech detection for spontaneous speech remains unexplored. This paper analyzes the influence of speech mode on pathological speech detection approaches, examining two distinct categories of approaches, i.e., classical machine learning and deep learning. Results indicate that classical approaches may struggle to capture pathology-discriminant cues in spontaneous speech. In contrast, deep learning approaches demonstrate superior performance, managing to extract additional cues that were previously inaccessible in non-spontaneous speech