The surge in Large Language Models (LLMs) development has led to improved performance on cognitive tasks as well as an urgent need to align these models with human values in order to safely exploit their power. Despite the effectiveness of preference learning algorithms like Reinforcement Learning From Human Feedback (RLHF) in aligning human preferences, their assumed improvements on model trustworthiness haven't been thoroughly testified. Toward this end, this study investigates how models that have been aligned with general-purpose preference data on helpfulness and harmlessness perform across five trustworthiness verticals: toxicity, stereotypical bias, machine ethics, truthfulness, and privacy. For model alignment, we focus on three widely used RLHF variants: Supervised Finetuning (SFT), Proximal Policy Optimization (PPO), and Direct Preference Optimization (DPO). Through extensive empirical investigations, we discover that the improvement in trustworthiness by RLHF is far from guaranteed, and there exists a complex interplay between preference data, alignment algorithms, and specific trustworthiness aspects. Together, our results underscore the need for more nuanced approaches for model alignment. By shedding light on the intricate dynamics of these components within model alignment, we hope this research will guide the community towards developing language models that are both capable and trustworthy.