Digital platforms such as social media and e-commerce websites adopt Recommender Systems to provide value to the user. However, the social consequences deriving from their adoption are still unclear. Many scholars argue that recommenders may lead to detrimental effects, such as bias-amplification deriving from the feedback loop between algorithmic suggestions and users' choices. Nonetheless, the extent to which recommenders influence changes in users leaning remains uncertain. In this context, it is important to provide a controlled environment for evaluating the recommendation algorithm before deployment. To address this, we propose a stochastic simulation framework that mimics user-recommender system interactions in a long-term scenario. In particular, we simulate the user choices by formalizing a user model, which comprises behavioral aspects, such as the user resistance towards the recommendation algorithm and their inertia in relying on the received suggestions. Additionally, we introduce two novel metrics for quantifying the algorithm's impact on user preferences, specifically in terms of drift over time. We conduct an extensive evaluation on multiple synthetic datasets, aiming at testing the robustness of our framework when considering different scenarios and hyper-parameters setting. The experimental results prove that the proposed methodology is effective in detecting and quantifying the drift over the users preferences by means of the simulation. All the code and data used to perform the experiments are publicly available.