Depression commonly co-occurs with neurodegenerative disorders like Multiple Sclerosis (MS), yet the potential of speech-based Artificial Intelligence for detecting depression in such contexts remains unexplored. This study examines the transferability of speech-based depression detection methods to people with MS (pwMS) through cross-corpus and cross-lingual analysis using English data from the general population and German data from pwMS. Our approach implements supervised machine learning models using: 1) conventional speech and language features commonly used in the field, 2) emotional dimensions derived from a Speech Emotion Recognition (SER) model, and 3) exploratory speech feature analysis. Despite limited data, our models detect depressive mood in pwMS with moderate generalisability, achieving a 66% Unweighted Average Recall (UAR) on a binary task. Feature selection further improved performance, boosting UAR to 74%. Our findings also highlight the relevant role emotional changes have as an indicator of depressive mood in both the general population and within PwMS. This study provides an initial exploration into generalising speech-based depression detection, even in the presence of co-occurring conditions, such as neurodegenerative diseases.